There is a wide spectrum of rasgueados in flamenco.
Perhaps the most basic aspects to consider are 1) wether the finger pattern matches the rhythmic pattern of the music, 2) the difference in sound between various strokes, 3) the final placement of your fingers at the end of the rasgueado and 4) personal idiosyncracies.
Note: please note that in all the cases I discuss here, I'm talking about rasgueado patterns that begin on the beat. The discussion gets considerably more complex if we consider rasgueados that do not begin right on the beat.
1) Matching stroke count to the rhythmic pattern of the music.
This is fairly straightforward. ami-i (ami down followed by i up) is a 4 pattern (i.e. it involves 4 different strokes). It works well with 16th notes (4 notes per beat). With each cycle of rasgueado you've gone through one full beat, or vice-versa. xami-i (xami down followed by i up) is a 5 pattern (5 different strokes) and therefore it works well for quintuplets. And ai-i works well for triplets (or any multiple of 3 for that matter).
2) Different strokes, different sounds
No matter how you cut it, different strokes will produce different sounds. An upstroke with i produces a different sound than a downstroke with i. With the upstroke you are attacking the strings from trebles to basses using a mix of flesh and nail. With the downstroke you are attacking the strings from basses to trebles with the top side of your nail.
One interesting aspect of this is is when you use a rasgueado pattern that, unlike what was described in 1), does not match the rhythmic pattern of the music. For instance, compare playing 16th notes with ami-i (ami down followed by i up) and playing those same 16th notes with xami-i (xami down followed by i up). In the first case, the i upstroke is always the 16th note immediately before the beat. The result is a consistent and stable sound. In the second case, the i upstroke changes places relative to the beat. It first appears on the 2nd beat, then on the 1st 16th note after the 3rd beat, then on the 2nd 16th note after the 4th beat, etc. The result is a "rolling" or "cascading" effect where the rasgueado doesn't seem to be entirely tied down to the beat.
Further, if you wish to play triplets, you might consider ai-i (ai down, i up). Or you might consider ami (only downstrokes). Since the latter uses only downstrokes, it is easier to obtain an even sound throughout. It is somewhat in disuse today, but it is featured fairly regularly in recordings of Montoya or Sabicas. Note that if you use the ami rasgueado, at the end of the rasgueado your fingers will be on the lower side of the strings, beneath the trebles. However if you use ai-i, at the end of the rasgueado your fingers are on the upper side of the string, above the bass strings. I'll discuss this in point 3).
The last thing to mention here is the use of the thumb. A common 3-stroke rasgueado pattern is the "marote" (also called "abanico"). The pattern is p up, am down (simultaneously in one single stroke), p down. This rasgueado allows for a very "full" sound, in the sense that it allows you to strike all 6 strings fairly equally. In comparison, ai-i will usually cover less strings. In fact, ai-i is most often played with the thumb anchored down to the low E string, which is thus not played at all. Context will determine which of the two is the more appropriate to use.
3) Finger placement at the end of the rasgueado
This will largely depend on each individual player. The main point is to consider what is played after the rasgueado and what is the most fluid transition between the two. For instance, the ai-i rasgueado is often used to play triplets in modern bulerias. It often appears as i-ai, namely, instead of starting on the beat with the a downstroke, you start with the i upstroke. This allows you to finish the rasgueado on the beat with an i upstroke. Your i finger is then perfectly placed to play an i downstroke on the off beat that follows. This is a very common technique to add syncopation in modern bulerias.
Another consideration is whether the rasgueado ends with a golpe. If a stroke is played simultaneously to a golpe, it is almost always the case that it will be a downstroke. One merely needs to try playing an upstroke with a golpe to understand why that is (it's not easy). Therefore, if the rasgueado is meant to end with a golpe, it is likely the guitarist will choose a rasgueado that ends with a downstroke.
4) Personal idiosyncracies
Each person will have their own preferences depending on what works best for them. Montoya sometimes played 16th-note rasgueado with pami (p upstroke followed by ami downstroke). He would obtain a very subtle, almost silky quality to his rasgueados that way. Nunez never uses x (pinkie). Pepe Habichuela plays a 3-stroke rasgueado that goes m-mi (m upstroke, mi downstrokes), which is uncomfortable for many but Habichuela somehow manages to draw considerable power from it. A common argument for ai-i is that it is easy to maintain a stable hand position. For players who enjoy this rasgueado, the m finger is usually perceived as a sort of central axis that stabilizes the hand. This is a matter of preference and for each guitarist to decide for him- or herself.