The chord we are discussing is often referred to as an "A shaped barre chord" and there as many ways to play it as there are to play the open A chord it is named after.
In your question, you expressed a desire and willingness to step out of your comfort zone and learn a new way to play this type chord if it will benefit you in the future! There is some value in playing a chord the way you feel most comfortable. But often it is also valuable to eventually learn alternate methods of fingering chords that might provide more flexibility in your playing. So just because a particular way to play a chord may not be the easiest and most comfortable way to play it today - does not mean that with practice, it can't become just as comfortable to play as the other.
As an example, when I first began to learn to play guitar, it was more "comfortable" for me to play a B flat chord using XX0331 playing only the four highest strings. But eventually I learned to play the full A shaped barre chord version of the B flat chord and it sounds much fuller. So my point is (one you alluded to) - don't let what is most comfortable today, halt your progress as a guitarist - IF you are capable of learning a new way to play a certain chord - one that opens new possibilities!
Having said that, I should point out that everyone's anatomy is different in terms of hand and finger size and shape. Certainly what is comfortable for one guitarist, may require too much of a stretch or a bend or contortion for another. Some folks play the A shaped barre chord the second way using only two fingers with the mini barre with the ring finger - because their fingers are too fat to squinch 3 together on one fret to use the first method, particularly as they move up the neck and the frets get closer together. Other folks may have such large finger tips that they find it impossible to bend the ring finger up to avoid fretting the high e string, so they don't use their ring finger for a mini barre. Perhaps they use their pinkie finger instead.
So the way you choose to play this barre chord may be limited by your unique finger and hand anatomy. However, if you are capable of learning to play the second version using your first and ring finger, I would encourage you to start practicing playing the chord that way until it becomes comfortable (may take some practice). I believe it gives you much more flexibility (no pun intended) in your playing overall.
First, the two finger version gives you the freedom to add more notes to the chord while you are playing it. For example, one thing I often do in a blues type progression is start with the A shaped barre chord as pictured in your second diagram using the ring finger as a mini barre to fret the 2nd, 3rd and 4th strings. Then alternately flatten my ring finger to add the first string to the strings barred with my ring finger. Then I can use my pinkie to play the first string one fret higher than where the ring finger is. If my fingers were long enough, I could play that same pattern using my pinkie finger to play the 4th string two and three frets higher.
From the two finger mini barre formation it is easier to add some fills and lead runs while playing the chord - or as you transition to the next chord. You are basically holding your fingers in a position to play most scales using two fingers. It's more common to play scales using your index, ring and pinkie fingers than it is to add your middle finger into the mix. It's easier to get in to the groove of just lifting your ring finger up and down than to try to figure out which of your other three fingers comes off to play which note. Plus, from the A shaped Barre position, you can use your pinkie in the fills as well.
One other compelling reason to learn the mini barre two finger version is that when you start playing this shape at around the 10th to 12th fret, it becomes very difficult for almost all males and most females to get three fingers on one fret (try it and you will see what I mean). So if you pass on learning to play it the two finger way, you may not be able to play the A shaped barre chord past the 7th, or 8th fret.
One thing I like to do as part of ending a high energy song with a bang, is to play the final ending chord as an A shaped barre - high on the fretboard and then slide the ring finger up for a nice descending fading crescendo effect. For example, if I am in the key of G, I may end the song by playing a G barre chord on the 10th fret where I am barring the B G and D strings with my ring finger on the 12th fret. I hit the chord with a hard strum - then slide my ring finger towards the headstock while still holding down those three strings. Yes that could be done with 3 fingers, but it is far more difficult.
Bottom line - if your hand and finger shape make it extremely uncomfortable for you to even attempt to learn to play the A shaped barre chord using the two fingered version, then find an alternate way to play the A shaped barre chord and forget about playing it past the point where your method will preclude enough fingers fitting in the smaller and smaller fret spacing. But if you feel like you could train your fingers to play this chord using the two finger method, it will offer far more versatility in the future and allow you to play this barre chord shape as high up the neck as you want to.
Good luck to you as you continue to improve your skills. It's a life long journey filled with great reward and satisfaction.