Your browser still provides a pretty unique fingerprint.

Tor uses either an isolated browser or VM. You'd be moronic to use the same browser both in and outside of the onion router.

you could use some privacy consious browser, like xombrero. for example: it has a feature to allow you to define a list of user-agents from which one is randomly selected on each request, allows you to use whitelist-mode in which you have to explictly allow cookies and js for each page.