All the answers offer good information but I like the one by wabisabied because it offers some logic behind the answer (even though I'd disagree with the actual statement it supports).
The fact is that every possible way to finger the chord serves a purpose. In choosing a fingering you need to satisfy a couple requirements: (1) does the fingering produce a good tone and (2) will it facilitate easy, optimal, movement from the chord to neighboring chords in the piece of music you are playing.
There are major problems with fingerings like (1, 2, 3) and (2, 3, 4) on the classical guitar in that these fingerings tend to force the E played on the second fret of the D string to be improperly fretted. Ideally, one should try and fret the note with the finger close to the fret that defines the boundary condition for a string "fixed" at two ends. It is a common misunderstanding that you can place your finger anywhere in the space between two frets to play the note defined by the higher numbered fret. This is not true. What happens when you finger the note too far back is you have a string that is free to slide on the fret that defines the note. This can cause severe buzzing and a weak sound with poor tone. This can happen on any guitar, electric or classical, but I find that the issue is very noticeable on the classical. The issue is exacerbated by the fact that the D string is wound which makes the buzzing more severe. In contrast the fingering (2, 1, 3) allows one to pinch the E on the D string right up to the fret. The A on the G string will be fretted slightly far back but more towards the center of the space between the frets.
With a little practice you might be able to correct the issue mentioned above using a fingering like (1, 2, 3) or (2, 3, 4) but there are other considerations. In moving from one chord to another you want the movement to be easy, smooth and, if you care about it as many classical guitarists do, avoids squeaking or scratching noises. You want to be able to release the strings (without completely opening the hand) and generate the new chord form quickly. As several answers point out this is facilitated by different fingerings for different progressions. A common movement is A --> E7, or I --> V7, and a common fingering for the E7 is (2, 1, 3) on frets (2, 1, 3) of the (E, G, B) strings. As you can see this is the same ordering of fingers as the (2, 1, 3) option for the A chord. So the movement allows you to keep finger 2 planted and 1 and 3 can simply slide back and forward by a fret. This is an optimal fingering for this movement. By the way, this implies that one might finger the same chord 2 or more ways in the same piece of music and we often do.
Other considerations are physiology, e.g. if your fingers are too large you may need to experiment with alternatives or find a way to get optimal movement and clean sound other ways. But the take away is that there is more than one "right way" to play all chords and the motive behind the choice is motivated by the two points made in the beginning of my answer (1) clean tone, and (2) optimal movement to other chords.