Our experience differs from many here, mine is 7 months so take this with a grain of very new mom salt :)
We lived in a studio through December of last year then moved a couple weeks before baby was born. We were SO happy we did. Our baby is a sleeper. A wonderful, wonderful sleeper. However, he is a NOISY little man. He grunts, kicks, coos, and even mumbles in his sleep. I barely slept a wink his first 6 weeks between the noises and nursing him. He also hated the bassinet and having him in our bed did not work well for us due to all those noises/movement. With our pediatrician's blessing, we transitioned him to his own room in our new 2-bedroom at 6 weeks, and we all slept great. He LOVES his crib and mobile. In fact he had previously woken 2x a night to nurse, the next week it changed to 1x a night, and he started sleeping through the night fully at 12 weeks old with very little to do with our doing anything about it. He still exclusively nurses, since he sleeps 12 hours a night I wake up around 5am and pump to relieve engorgement. He's chubby, healthy, and at 7 months sleeps 12 hours a night and takes 2 naps of 1-2 hours each day. There is no way he would do that if he didn't have a separate space -- while he sleeps THROUGH loud noise and hubbub, he is very alert and curious and needs a quiet dark room to FALL asleep in.
The tradeoff is of course the extra money on housing and commute. My husband still takes public transport/walk to work but his commute did go from 40 to 60 minutes (NYC and he works in FiDi so comparative to others it's a *good* commute even though it sucks, he works on train). In our case we decided to buy since the math came out in favor of doing that, but it meant a move to the very-close-in suburbs rather than an outer borough, and total monthly housing cost is up even though the principal to our mortgage means we pay less that disappears from our assets.