Strictly better? No.
One of the major points of Disguise Self is that it can not only alter your appearance (via illusion), but your clothing and equipment as well.
It's important to note the inverse of this: Alter Self does not specify that it modifies your clothing or equipment. This means that, depending on how severe your alterations are, you may no longer fit into your armor and your clothing may clearly no longer fit you, depending on how simulationist your DM is on the topic. This is especially important if using the "Variant: Equipment Sizes" rule on PHB p.144:
In most campaigns, you can use or wear any equipment that you find on your adventures, within the bounds of common sense. For example, a burly half-orc won’t fit in a halfling’s leather armor, and a gnome would be swallowed up in a cloud giant’s elegant robe.
The DM can impose more realism. For example, a suit of plate armor made for one human might not fit another one without significant alterations, and a guard’s uniform might be visibly ill-fitting when an adventurer tries to wear it as a disguise.
Using this variant, when adventurers find armor, clothing, and similar items that are made to be worn, they might need to visit an armorsmith, tailor, leatherworker, or similar expert to make the item wearable. The cost for such work varies from 10 to 40 percent of the market price of the item. The DM can either roll 1d4 × 10 or determine the increase in cost based on the extent of the alterations required.
Even if your equipment does fit you after the effects of the spell, any well known gear or accessories may still let you be identified, especially if they're more well known then your actual physical attributes.
There are a few other considerations as well.
One of them is that both Alter Self and Disguise Self can be used at the same time, to enhance the illusion with actual physical changes underneath it. Do note that this is only possible because Disguise Self does not require concentration, which is another point in its favor over Alter Self, which does. This means Alter Self can fail earlier than intended (especially in combat or while under stress), while Disguise Self will last the duration under most conditions, and still allows you to cast other concentration spells.
Another is comparing how Disguise Self and Alter Self interact with height & size.
Alter Self actually changes your height, while Disguise Self only creates the illusion of a height change, keeping you your usual size. This might matter if your DM actually cares about character height in certain situations rather than just your size.
In addition, Alter Self restricts you to only changing your appearance to a creature of the same size with no other restriction on maximum height gain/loss, while Disguise Self only has a restriction on height change rather than size change.
For example, with Alter Self, you could change the shortest possible dwarf into the tallest possible goliath, whereas with Disguise Self, you could make a dwarf appear to be a halfling (so long as you're not trying to change your height by more than a foot in doing so).
Overall, I'd probably rate Alter Self better than Disguise Self in some combination of the following situations:
- There is plenty of time to make preparations in advance, including having an appropriate alternate outfit ready.
- You are unprepared, but you only need minor superficial changes with no drastic change such as size, making the lack of alternate costume not an issue.
- You are in no danger of having your concentration broken for the next hour, nor are you likely to need to cast any other Concentration spells.
- You are likely to be thoroughly inspected for some reason or another.
In other situations, there is a chance Disguise Self may be the more appropriate spell. In a situation requiring an emergency drastic appearance change (clothes, size, and all), for example, I would much prefer Disguise Self as my option.
I think I would compare it to another spell that offers similar benefits: Invisibility.
Invisibility grants advantage in combat once, upon the first attack. Also, Invisibility requires concentration. Neither of these are required by Disguise Self.
Given that Invisibility is considered the more powerful spell (2nd level vs. 1st), it seems problematic if Disguise Self were to grant advantage continuously with no concentration requirement.
Here is my opinion:
- Make Disguise Self require concentration, at least in combat.
- Give a saving throw before the first strike to see if the disguise is discovered, minus of course the subject being hidden or likewise indiscernable. (The justification for this is that in combat, you pay attention to details since your opponent is trying to kill you, thus triggering the "fail to hold up to physical inspection.")
- After the first attack, the deception is automatically discovered and negated thereafter.
The tail, just as the example of becoming thinner, would no longer be visible. But since you put emphasis on invisible it should be noted that in Dungeons and Dragons 5e, invisible is not exactly equivalent to not being visible. It is a specific game term with specific game consequences. It is a condition.
Nothing in the spell "Disguise Self" gives the condition invisible. So RAW you are not treated as such.