Off the top of my head: The back button doesn't work right, saved passwords don't move over, clicked links (if they work at all) keep you in the new application instead of your browser, the places you're taken are left out of your browsing history, you can't bookmark the destinations. Basically all browser functionality that isn't "render the page" gets lost -- it's the same problem you'd run into if you use Chrome for everything and a link from Outlook pops up the page in IE: It _works_, but the ecosystem you've built up for yourself is gone.
