(Note: Guillaume F. caught a significant error in my equation formulation, so this answer changed to reflect this.)

In almost all pure DPS comparison scenarios, Bless is the winner if they have a good Dex save. Faerie Fire is better if they have a bad Dex save. The break even point is about when they need to roll a 10 on their Dex save.

When the target of the Faerie Fire spell makes their save with a roll of 10 or less the Bless becomes the better spell for raw DPS buffing. By a save on 9 or less, Bless is the clear winner.

Here it is in a color coded graph for you.

Down the left hand side we have the attackers target number - the number they need to roll on a d20 to hit. The first column has your DPS multiplier with no spell, the second with bless, and the third with Faerie Fire in effect. There numbers go to 24 because the bless spell allows you to technically roll up to that number ( a 20 on the to hit dice, and a 4 on the bless dice.)

To the right of that we have the enemy's target save numbers in descending order across the top. That is to say the target number on the dice where they make their save. Note that the target number of 21 on the table represents where the opponent cannot make the save.

Where the chart is green, Faerie Fire is better than Bless, where it is yellow Faerie Fire is worse than Bless, but still better than nothing, and Red you just wasted a spell slot on Faerie Fire (on average), because the expected increase in damage from FF is no better than having cast no spell at all.

It's the Dex save that makes or kills Faerie Fire's DPS. If the spell lands, it is hands down better than Bless, so if your target has an average or higher chance of failing their Dex save, go with Faerie Fire.

Even if they might save, Faerie Fire might still be the best choice, but this analysis has certainly changed my thinking on how I would use it.

Read on for the detailed explanation.

And Now for Some Math

I think with a simple removal of some superfluous information, we might be able to simplify the problem to where we can get our hands around it.

OK - in 5e combat, when you make an attack roll, your average expected damage per attack (which I call DPS for MMO terminology reasons) boils down to a calculation of your chance of hitting without critting times your average damage plus your chance of hitting with a crit times twice your average damage. I know that this is not 100% accurate since damage modifiers are NOT doubled on crits, but it's close enough for the purposes of this analysis.

Lets express that as an equation:

$$ AverageExpectedDamagePerAttack (DPS) = (P(HITnocrit) \times AVGdmg ) + (P(crit) \times 2 \times AVGdmg ) $$

This translates to

$$ DPS = AVGdmg \times ( P(HITnocrit) + 2 \times P(crit) ) $$

Since literally anyone in the party can benefit from either spell, why don't we just take the average damage part out of this equation. It certainly doesn't matter for purposes of comparing the spells. If you want to know what your specific DPS will be just multiply this new number by you average damage.

So now we have:

$$ DPSmultiplier (DPSm) = P(HITnocrit) + (2 \times P(crit) ) $$

Now comes the second jedi mind trick. Stick with me on this one, as I may have trouble explaining it well. Leave comments if you can explain it better.

For comparing the two spells we were able to ignore damage because for any given individual the only variable we want to test here is what effect does changing the spell in play have for that individual's outcomes.

So we can do the same for chances to hit if we abstract away the targets AC and the attackers to-hit bonus and we just look at what they need to roll. Why? Because when comparing the two spells - that's all that matters. What do I need to roll on a d20 with bless to hit (or crit) vs. what do I need to roll on a d20 with faerie fire to hit (or crit).

So imagine I have a 14 Str (+2), and a prof bonus of 2 and I swing my mundane sword at a mage with mage armour up (AC 13). I need to roll a 9 in order to hit. I call that number the Target Number. My Target Number is 9. It will be 9 under a bless spell or with a faerie fire spell. But if we do the calculations using target number, we no longer have to know the AC and to-hit bonuses for every scenario. With this abstraction, we can collapse the problem space down to comparing only 20 numbers.

Going back to our equation, on a normal d20 roll, if our TN was 9 as in the above example. you would hit (no crit) on a roll of 9 - 19 which 11 times out of 20 or 55% of the time, and of course you would crit on a 20, or 5% of the time

$$ DPSm = P(HITnocrit) + 2 \times P(crit) $$

$$ DPSm = 0.55 + 2 \times 0.05 = 0.55 + 0.1 = 0.65 $$

Are you with me still? Good.

Now let's do Bless for our intrepid mageslayer.

With a bless spell in effect there are 80 potential outcomes. (d20 × d4). If you roll a twenty on the d20 - that's a crit no matter what you roll on the d4 - so 4 out of 80 times 5% of these will be crits. Now if you roll a 1 on the 1d4, you can roll a 8 - 19 and still hit without a crit, which is 12 ways to hit without a crit. By extrapolation you can see that a 2 on the d4 gives 13 ways to hit without a crit; 3 gives 14; and 5 gives 15. So we have 54 ways out of 80 or 67.5% to hit without a crit.

Plugging that into our equation we get:

$$ DPSm (Bless) = 0.675 + 2 \times 0.5 = 0.675 + 0.1 = 0.775 $$

The math gets a little more complicated with Faerie Fire but it is based on the same principles. Suffice to say, with FF and a TN of 9, your chance to crit is almost double at 9.75%. And your chance to hit without critting is also elevated at 74.25%

Plugging that into our equation we get:

$$ DPSm (Faerie Fire) = 0.7425 + 2 \times 0.975 = 0.7425 + 0.195 = 0.9375 $$

It's looking good for Faerie Fire. Advantage really is a helluva thing. But things are not so rosy when we factor in the saving throw. If the saving throw succeeds, the player drops down to normal DPSm. Meaning, we should allocate the DPSm based off the targets chance of making the save. If the target has a 50% chance of saving, then we allocate half of the DPSm under FF, and half of the normal DPSm. This buoys the FF numbers somewhat.

In the charts below I calculated the raw Faerie Fire numbers (ie after the spell lands), and the DPsm if their save target number is 16, 11 and 6. (ie 1/4, 2/4 & 3/4 chance of saving respectively). Since either the spell lands and does the increased FF damage, or it doesn't land (and therefore normal damage), the spell save can't take Faerie Fire's DPSm below that of a normal d20 roll. So that is accounted for in the charts. For example: If your to hit target number is 12, and the enemy saves 3/4 of the time, three times out of 4 you will be doing normal damage (which is 50% multiplier), and 1/4 or the time you will get FF damage (a 79.5% multiplier). 3.4 * 50% + 1/4 * 79.5 = 57.375%. So if you look in the last column (Save on a 6 or better) under the row with a Target Number of 12 you can see that multiplier.

Now for the Charts aka Who Charted

\begin{array}{|c|c|} \hline \text{Target Num} & \text{normal DPSm} & \text{Bless DPSm} & \text{FF DPSm} & \text{FF DPSm (save16)} & \text{FF DPSm (save11)} & \text{FF DPSm (save6)} \\ \hline 1 & 100.00 \% & 100.00 \% & 109.50 \% & 107.13 \% & 104.75 \% & 102.38 \% \\ \hline 2 & 100.00 \% & 100.00 \% & 109.50 \% & 107.13 \% & 104.75 \% & 102.38 \% \\ \hline 3 & 95.00 \% & 100.00 \% & 108.75 \% & 105.31 \% & 101.88 \%& 98.44 \% \\ \hline 4 & 90.00 \% & 98.75 \% & 107.50 \% & 103.13 \% & 98.75 \%& 94.38 \% \\ \hline 5 & 85.00 \% & 96.25 \% & 105.75 \% & 100.56 \% & 95.38 \% & 90.19 \% \\ \hline 6 & 80.00 \% & 92.50 \% & 103.50 \% & 97.63 \% & 91.75 \% & 85.88 \% \\ \hline 7 & 75.00 \% & 87.50 \% & 100.75 \% & 94.31 \% & 87.88 \% & 81.44 \% \\ \hline 8 & 70.00 \% & 82.50 \% & 97.50 \% & 90.63 \% & 84.75 \% & 76.88 \% \\ \hline 9 & 65.00 \% & 77.50 \% & 93.75 \% & 86.56 \% & 79.38 \% & 72.19 \% \\ \hline 10 & 60.00 \% & 72.50 \% & 89.50 \% & 82.13 \% & 74.75 \% & 67.38 \% \\ \hline 11 & 55.00 \% & 67.50 \% & 84.75 \% & 77.31 \% & 69.88 \% & 62.44 \% \\ \hline 12 & 50.00 \% & 62.50 \% & 79.50 \% & 72.13 \% & 64.75 \% & 57.38 \% \\ \hline 13 & 45.00 \% & 57.50 \% & 73.75 \% & 66.56 \% & 59.38 \% & 52.19 \% \\ \hline 14 & 40.00 \% & 52.50 \% & 67.50 \% & 60.63 \% & 53.75 \% & 46.88 \% \\ \hline 15 & 35.00 \% & 47.50 \% & 60.75 \% & 54.31 \% & 47.88 \% & 41.44 \% \\ \hline 16 & 30.00 \% & 42.50 \% & 53.50 \% & 47.63 \% & 41.75 \% & 35.38 \% \\ \hline 17 & 25.00 \% & 37.50 \% & 45.75 \% & 40.56 \% & 35.38 \% & 30.19 \% \\ \hline 18 & 20.00 \% & 32.50 \% & 37.50 \% & 33.13 \% & 28.75 \% & 24.38 \% \\ \hline 19 & 15.00 \% & 27.50 \% & 28.75 \% & 25.31 \% & 21.88 \% & 18.44 \% \\ \hline 20 & 10.00 \% & 22.50 \% & 19.50 \% & 17.13 \% & 14.75 \% & 12.38 \% \\ \hline 21 & 10.00 \% & 17.50 \% & 19.50 \% & 17.13 \% & 14.75 \% & 12.38 \% \\ \hline 22 & 10.00 \% & 13.75 \% & 19.50 \% & 17.13 \% & 14.75 \% & 12.38 \% \\ \hline 23 & 10.00 \% & 11.25 \% & 19.50 \% & 17.13 \% & 14.75 \% & 12.38 \% \\ \hline 24 & 10.00 \% & 10.00 \% & 19.50 \% & 17.13 \% & 14.75 \% & 12.38 \% \\ \hline \end{array}

OK. Lets do a quick reading on our chart.

Our fighter has been joined by a rogue and bard, and they roll up on beast of unknown origin. They need to roll a 6, 11, and 16 to hit the beast respectively. (not realistic I know, but roll with it) Should the bard cast bless or faerie fire (for some reason this bard took bless as their spells secrets spell), assuming the beast will save only with a 11 or higher on it's roll?

Well FF will increase the fighter's DPSm to 91.75%, the rogue's to 69.88% and the bard's would increase to 41.75% over normal. Whereas bless takes the DPSms to 92.50%; 69.88%; and 42.50% respectively.

Bless it is, but just barely.

More realistically, assuming the same target save, it the to-hit target were clustered in the center (as they likely will be using bounded accuracy), FF, becomes the option. For this save target, very high and very low ACs lend themselves to using Bless, average ACs to FF.

Note that if the save target for the beast was 16 - then Faerie Fire becomes the better choice, unless your foe has a great AC. And you should always use bless if you need to roll a 20 to hit your target.

On the other side, if your foe has slightly better than 50% odds of making their dex save, bless is the better option in almost all cases.

###Edge Cases

The math gets a little tricky when we need a 20 (or above) to hit, or when we only miss on a 1. For example, if you only miss with a roll of a one, a roll that always misses, then the addition of the bless spell can never offset the fumble. So there the DPSm is the same for bless and a regular attack roll. This also applies when your target number is 2, because a target number of 2 to hit means, in effect, you only miss on a roll of a 1. And if you look at the rows for TN of 1 and 2 you can see that they are identical. (Technically you can never roll a 1 while under the effect of a bless spell. The lowest you can roll is 2, but that is still a fumble because you would have rolled a 1 on the d20)

Faerie Fire, on the other hand gives advantage, which reduces your chance of rolling a 1, because you would need to roll snake eyes on two d20, which is a 1 in 400 occurrence. Still the increase to DPS is very slight, but it is enough to make Faerie Fire to superior choice when you only miss on a fumble. This makes sense, because with bless you still fumble 1 in 20 times, whereas if FF sticks, it drops your fumble chance to 1 in 400 (as noted above)

There are similar distortions at the bottom of the table due to the fact that a 20 will always hit and do double damage. It is interesting to note that if you need a 20 exactly to hit, then Bless is always the choice, but if you need a 21 or higher, FF is again a viable option.

So all this begs the question:

When is Faerie Fire useful?

• It is an area effect spell, so if you can blanket a whole bunch of opponents, there are bound to be some who fail the save.
• You opponents have low Dex saves - maybe they are restrained or immobile.
• Your opponents are invisible, in darkness, fog, or have some other way of giving you disadvantage.
• You have a rogue in the party who wants to make with the stabby stabby and no one else is near them.
• You have a Champion in the party who crits on a 19 or better.
• You have a Barbarian and/or Half Orc who gets extra damage on a crit.
• You have a large party of people (5+) who like to make attack rolls, not control the battlefield, or the like.
• You can impose disadvantages on the enemy's dex or magic saving throws.
• When they have a 50% chance or better of failing their save (generally - see chart).

When is Bless useful?

• When fighting opponents that will make you roll saving throws.
• When fighting one or two big bads - better to buff your team than to risk it all on a save.
• When there are not more than three attackers needing a buff in your party.
• When they have a 50% chance or better of making a dex save (generally - see chart).

The highest level spell I could find that uses a melee spell attack to deal damage is Mordenkainen's Sword (level 7). The relevant part of the spell reads:

When the sword appears, you make a melee spell attack against a target of your choice within 5 feet of the sword. On a hit. the target takes 3d10 force damage. Until the spell ends, you can use a bonus action on each of your turns to move the sword up to 20 feet to a spot you can see and repeat this attack against the same target or a different one.

However, it's worth noting that Plane Shift (level 7) requires a spell attack and a save to let you banish an enemy, which is equivalent to killing them most of the time:

You can use this spell to banish an unwilling creature to another plane. Choose a creature within your reach and make a melee spell Attack against it. On a hit, the creature must make a Charisma saving throw. If the creature fails the save, it is transported to a random location on the plane of existence you specify.

Otherwise, for a wizard, there aren't really spells that start at high level that require an attack roll.