Seems there was a time when Facebook was the most popular means of marketing, promotion, and communication with friends, fans, and potential talent buyers. But I've always maintained a website for my bands just to cover all bases. Now I'm getting the impression that Facebook is becoming kind of a drag for a lot of people, so a web site might be more important than before. Also, since I work with a lot of private/upscale event planners, I think many of my clients are a little more impressed with the web site and they consider it somehow more "professional," an extra effort on my part. Just an intuition, no hard data to support it, but it seems to help with some clients. Upscale clients can be funny, and the possible misconception that you went the "cheap route" with FB and no website can influence them. Obviously, you link the two formats together and it makes for a pretty wide and thorough on-line brush stroke. In competitive markets like mine, you do everything you can.
Your target client and audience has a lot to do with it. If I wasn't targeting upscale private events, I'd probably shut the web site down and just use FB. I use Wix.com, and it's not expensive, but it's not cheap either for my budget. I'm also on GigSalad and GigMasters. This stuff adds up fast.