Personally I think it's good to have both. AW has a lot of traffic, but there are a lot of rules and regulations about what we can and can't say. With your own website, you have somewhere to send people for further info that's less likely to be blocked by firewalls or adult content filters etc., and with a bit of SEO you can make sure you're on the first page of Google's search results using relevant keywords. You perhaps also look a bit more professional/serious? I'd say it's money very well spent.
I have a website, I dont ask people where they got my details but it has a lot of page hits in the admin section so I know plenty look at it, then again my aw has too so who knows, Im on a lot of directories also and apparently in some contact magazines although im not bothered, they have my correct number and thats all thats needed