I’ve used BBEdit for years, but TextMate blows it away (except for one thing). TextMate’s bundles and plugins really make it shine. The only thing I miss in BBEdit is the FTP browser, which lets me open files directly from an FTP server, rather than using a separate FTP client.
Ciarán Walsh offers some great TextMate tips in his blog, including some features I wasn’t aware of. In his latest entry, he discusses the HTML bundle.
One unique feature of TextMate is that bundle commands can interact with the selection intelligently. For example, ^< (shift-ctrl-<) with no selection will insert opening and closing <p> tags with the first 'p' selected. If you change it to something else, the closing tag will reflect it. As far as I know, there's no way to do anything like that in BBEdit. If only TextMate added FTP support, it would be perfect.