I rented from something of a private renter who just owned one building, but ran it very professionally like you would see in a large company. I've heard both good and bad when it comes to the large companies; on one hand, they have more selections, are likely better organized, and are probably more available, but on the other, their service might seem sub-par, or their units may be sub-standard.
Personally, I'd avoid a private contractor that advertises through craigslist, or just has a sign out in front of something like a house or a duplex. I've heard all kinds of stories that involve the manager being a prick to downright un-liveable apartment units. Part of that though is always a gamble, regardless of where you rent.
My suggestion would be to find out what companies there are that rent buildings. That would be your safest bet, though they might have some strict leasing requirements, like signing a 12 month lease or not allowing moving during winter months.