Artifacts, ego types, and most normal objects have to pass a depth check before being generated. But nothing in the game has a depth below 100, so there would be no difference between 100 and 200 from that perspective.
It might be easier to find weapons with higher +to_hit and +to_dam values, or armor with higher +ac, but that would be unlikely to matter much, because you'd be using artifacts anyway.
I don't know if rings of speed take dungeon depth into account. Most other types of bonuses in the game are capped. (e.g. a Ring of Constitution +6 is as good as Rings of Constitution get.)
Dungeon level 100 doesn't have stairs down, but you can get to level 101 by falling through a trap door on level 100.