So Xanathar's Guide has given us the Find Greater Steed spell. This is in some way better than the Find Steed spell.
This can be inferred from the names of the spells and the sample mounts it gives us; Find Steed says:
…the steed takes on a form that you choose: a warhorse, a pony, a camel, an elk, or a mastiff. (Your GM might allow other animals to be summoned as steeds.)
And Find Greater Steed says:
…the spirit takes on a form you choose: a griffon, a pegasus, a peryton, a dire wolf, a rhinoceros, or a saber-toothed tiger.
My issue is with the fact that it is not clear what the difference between these spells actually is. It does not explicitly state that one of these spells has a type restriction (such as Find Steed only allowing beasts, whereas Find Greater Steed allowing monstrosities, for example; leaving aside that you then override that type with fey, fiend or celestial), having a restriction on flying or other speeds, or having a max CR in either case.
We can derive a max CR from the sample lists, see Dale M's answer to this question, but it isn't explicitly stated. For things like druid's Wild Shape this is explicitly laid out, but it is not made as clear for these spells.
However, the Find Steed spell description does state "(Your GM might allow other animals to be summoned as steeds.)" Also that Find Greater Steed lacks this kind of statement, implying that for Find Greater Steed, you must use on one those suggested, whereas Find Steed has more options.
So is the only difference an implied CR increase based on the sample creatures, even though Find Steed wasn't explicitly CR capped to begin with?
Or, is there nothing stopping the DM from allowing anything they like* for Find Steed, thereby making Find Greater Steed completely redundant?
This is also an issue for characters that already have more interesting mounts for Find Steed prior to the Find Greater Steed spell being "released", so such characters who were awarded, say, a Pegasus by their DM as a Find Steed steed would never have to consider casting the Find Greater Steed spell.
*Obviously the DM can allow whatever they like and override the rules completely, but even so the Find Steed spell specifically calls attention to the DM's power in this case.
Best Answer
Find steed is intended to give different options than find greater steed
First, some unofficial guidance per Jeremy Crawford, lead rules designer:
So, the designer states that FGS provides access to options that FS does not allow. This seems to imply that, though unwritten, there was the assumption that the DM adjudicating FS would not allow the player to summon creatures much more powerful than the ones provided already in the list (which range from CR 1/8 to CR 1/4). Otherwise there would be no restriction on the steeds since "Your GM might allow other animals to be summoned as steeds." technically enables anything.
Previously it may have made sense to allow stronger steeds using find steed
Before Xanather's Guide to Everything was published, it makes a lot of sense to use the DM leeway built into the spell to summon more powerful creatures in DM-allowed cases. For example, a 20th level paladin seems powerful enough to be able to cast a spell giving them something other than mundane animals.
Specifically, because there were no other options available to summon more powerful steeds, DMs had to resort to using the spell in this way because there was no other way for a paladin to summon a steed higher than CR 1/2.
Even Crawford explicitly said that the DM could choose what was summoned (before XGtE):
Find greater steed should now be the only way to summon more powerful steeds
As, time goes on, D&D is always changing. Rules get added and changed. Errata gets published, holes get patched, etc. In this case, a new spell was added: find greater steed. This spell was clearly added with the intent to be a more powerful option than find steed:
The very existence of find greater steed means that there was a limitation to begin with on find steed or that one was intended. What reason would the designers create a spell that would essentially replicate the effects of a lower level spell with no benefit? Why create a "greater" version if it can already be done with the original version? The answer: this is because the intent is for find steed to only be used with less powerful steeds while find greater steed would work for more powerful ones.
Another reason supporting this is that RAW imply that find steed can summon any steed with a 2nd level spell only. However, since the designers clearly have rated summoning pegasi and pertyon (eg) as a 4th level spell-worthy ability, it seems that continuing to allow this would mean that you are severely bending the spell slot economy for this spell only. Thus, making find steed much more powerful than comparable 2nd level spells. This is generally not seen as a good thing, and it would seem not to be in the interest or intent of the designers of the game to want/allow this.
What to do if a DM has already allowed more powerful steeds with find steed?
DM should do the same thing that happens when any new rule is added or old rule changed or patched: either accept the new going forward or ignore it and keep doing the way you were doing before.
Regardless of how DMs previously ruled, going forward we now have an official option that enables doing the things DMs previously had to adjudicate using the lower level spell. This provides the advantage of some additional clarity and allows for the game to be played according to the designer's intent.
If intent isn't important or if it would create an issue for the DM or players, the DM could, of course, just ignore the new spell and keep adjudicating with whatever houserules they previously used.
tl;dr
Rules as intended suggest that only FGS be used for more powerful steeds and FS used only for weaker ones.
but
RAW would technically still allow the DM to choose a mount covered in FGS with FS.