Like Terri S., I rely on AirBnB at times, but I also check hotels.com, as I am a member of that site, and Choice Hotels, because again, I am a member of that hotel group. If I book through hotels.com, after a certain amount of bookings, I can get a free stay, and same with my Choice Hotels membership. I still do shop around for the lowest price, though. If AirBnB is significantly cheaper, I will go with that, over either of the other 2. If I don't want to share a small home with others or I don't see any AirBnB sites that really do anything for me (whether they aren't charming, seem to be in an inconvenient area, or the hosts don't say they are kid-friendly), then it will come down to who will give me the better price, Choice Hotels or through a hotel on hotels.com.
Many times, the hotel has offered to match the price that hotels.com has offered, so I get the perks of dealing with the hotel directly, at the low price I had seen on a competitor's site. Either way I collect points, as I mentioned. Like Terri S. and Elena B. both said, sometimes, booking on hotels.com or through a third party can be a mission when trying to cancel a hotel, even when you're within the cancellation period. Sometimes just getting someone on the phone alone to request a cancellation is a hassle. My friend booked through Expedia.com once and we got sick and they gave us hell when trying to cancel the trip. We had to offer to send a doctor's note as proof, and whine and complain until we finally got them to accept changing our travel date without penalty. If you're 100% sure of traveling, that you will want to stay at that particular hotel, and don't want to do the AirBnB thing, then booking through a third party should be fine.