That's a good point, although I think a satisfying way to handle this is simply to open a new tab if the current one is unsaved.One situation never occurs in a browser but is very, very common in an editor: What happens when you have unsaved changes in the current file then open a new file in the same tab? Should the editor auto-save the current file? Discard changes? Ask the user? None of those approaches are very satisfying.
I do think that TextMate needs a way to somehow scroll the tabs in a manner similar to Firefox. Not being able to see and re-arrange tabs to the right of the viewport is really annoying.