I'm definitely a Gmail user. Not only for Volunteering for dA, but in my personal life, too.
Having my emails thread together is invaluable, the chat option in the gmail engine is QUICK, unnoticeable from across the room, and superb for something like an office setting. As well, there's numerous Firefox stylish and Greasemonkey codes to clean up ads, give more space, recolor/restructure the interface... and more!
I used to use hotmail wayyyyyy back when. Wasn't a fan then, and am certainly not now. Folders are nice, sure, but when it comes right down to it they're absolutely unnecessary when one can simply type in a keyword to see every email associated with it. Tie all of the usefulness of gmail together with Google Calendar and Google Docs... and what you have before you is an unstoppable force of awesomeness!!
Hm.... I've used both and I'd personally go with Gmail on this one.... It's well organised, places emails with the same heading into a single thread so easy to access, has a chat system built right in so that if you don't want to bother downloading it proper you don't have to. It's also easy to use and lets you label the important stuff, oh, and it has lots of space...
Hotmail on the other hand is more visually pleasing in my opinion and has slightly more functions than the gmail conterpart (if I remember correctly) though has less space. Its messenger function also has more personal customisstion options while gmail does not. Also, I find the hotmail messenger to be slightly more reliable than that of gmails in that gmail often looses connection (if you didn't bother downloading it) and it takes a couple of seconds for it to reconnect nad if you did download it, it looses its connection once in a while (not really that often and not really worth worrying over or noticing or mentioning) which is about once every month or longer. Note that the connection lost maybe due to the crappy internet I have and may or maynot affect you. That being said, hotmail is more disorganised than Gmail and has less space.
I said Hotmail, just because I never had any problems with it.
My parents made me switch to Gmail. While Gmail is nice and all, it doesn't allow me to put things into folders (or, at least, I haven't figured out how to do that). Yes, you can mark things so that they belong to a certain category, but I can't put them into folders.
Also, Gmail doesn't work as well on slower computers. Our computer at home is pretty slow, so Gmail doesn't always function right. And, Gmail doesn't work well through proxies (which I use at school).