Earlier quoted context omitted.
Off the top of my head - offline support, PGP support, multi-account support, decent mail-list/threading support, separation of client from service provider.. I'm actually quite a fan of the gmail interface; it is one of the most usable webmail experiences in my opinion (I use google apps both at work and for personal use). For day-long usage, I'd rather stick with mutt/vim.
Folders. Didn't Gmail kill folders?
If you only apply only one label to a mail at a given time, it works as a folder would do just fine.