this is a very general question, it really depends on a few things ...
1. how old is the building ??
in newer buildings, the building code is far more strict and followed by the builder. this leads to stronger floors, roofs, and walls.
2. can you fit the bigger tanks that you might want on an exterior wall ??
setting up on an exterior wall will provide the most stable place to set up.
3. figure out which way the floor joists run and set up across as many as possible.
doing this will disperse the weight and pressure across more of the floor and you will have more joists (usually 2x8s or 2x10s) to support more of the weight.
with that being said ... i lived in a brand new apartment a few years back, and i kept a 6' 125 with DSB and 200+ lbs of LR, a 55, and an 8' frag tank ON THE SECOND FLOOR !!
if the planning is right, and the building permits it ... apartment living should have no affect on what size tank you can go with.