Due to my impending divorce, I find myself in a second floor apartment. I had my safe professionally moved (900 pounds, empty). Although a neighbor might notice the noise of a break-in and report it, I think it is pretty unlikely that the mind-your-own-business people in this building would do so unless it was pretty blatant. I know I made a lot of noise when moving in. Nobody came out to look.
One consideration: when you live in an apartment, your risk of fire goes up simply because there are more people, more stoves, more hot water heaters, more furnaces, more flamables. So I think an apartment dweller has even more reasons to have a safe than a homeowner. Especially one with a high fire rating.
I did check with my landlord before I put the safe in. The building is only about four years old. He had no problem with it at all. I don't have any sense of the floor or stairs not being strong enough.