A T1 doesn't compare to a good cable connect anyway... A T1 is only 1.544 megabit (up/down). I'm getting 3 Mbit down/384k up on my cable connect.
They are right though, it's probably a single shared T1 because the price of a T1 monthly is usually around 500 dollars before mileage. Now if noone in your building is taking advantage of it, then you'd have a pretty good connection for a measly 40/mo. But if you have 20 people using it and even a few of them are bandwidth hogs then you might as well be using dialup. Well... not THAT bad, but you get the picture. You'd be sharing it with others which could be good or bad. I'd guess you'd PROBABLY see 40-50k/sec average if it's under moderate load.
It couldn't hurt to try it if it's your only option. Since you live in an apartment building, more than likely they'd be against you putting up a satelite dish or wireless antenna so that might BE your only option.