In my HRE test game with them they looked to be on track to sweep Spain and Britain and even after having invaded Portugal and Scotland and starting in on Andulusia they gave me a solid fight despite me having prepped over forty retinues, majority knights. Granted, that was partially because travel time forced me to march my levies in four seperate groups and their doomstack obliterated one of them, but it was still fierce. However, I also tried swapping to control them, and their long-term prognosis was not good even before I smashed them. Problems:
1. There's only a couple nonreinforcing doomstacks, which obviously won't last forever, and they aren't a super unit type like horse archers.
2. Unlike the Mongols, the area they arrive in is a different religious group. That means they either eat conquered: different religion or eat infidel relations penalties. Either way the conquered areas are between useless and counterproductive for decades, which is a problem when the doomstacks run out.
3. They don't have any special mass conversion powers, they don't have many courtiers, and the combined culture+infidel relations penalties are too high to demand landed vassals convert en masse.
4. This is probably just my game, but the Emperor was celibate.
Fixes:
1. can stay if the others are fixed, I guess, but there's a whole Aztec Empire on the other side of the ocean. Ideally they'd have a strong vasslized merc contingent that's not tied to a specific province to represent that
2. Not a problem if 3 is fixed
3. There should really be a "ordered everyone to convert to their blasphemous gods and ripped out the hearts of those who refused to comply" event/decision. Convert the province to Aztec and apply a substantial "Large chunks of the population had their hearts ripped out recently" penalty. Ideally a total penalty of -70% between that and cultural to everything once the basic recently conquered penalty is gone.
4. Make this not happen. Also, create wives and children for the Aztec leadership.