That depends. From what I've read and experienced there are pros and cons to each way. I always look online to see what's showing but find it takes forever to get through the screens (even on the fastest cable etc.) but I do know that sometimes blocks of rooms are shown there that aren't necessarily showing up on CRO screens for various reasons (especially if you are looking at Travelocity or another travel site). You can enter your room preferences yourself online which probably is better than simply telling CRO. Some people have great experiences online booking and get what they want but others have their reservations messed up.
For what it's worth, I always book on the phone with CRO. I like to ask questions and probe a little about availability of discounts etc. And I like to get the name of the person I'm working with and be able to speak with a supervisor if necessary as I had to with our current reservation.