uTorrent will get you faster speeds if you can get it to work optimally. I think it handles DHT better or something. I like both clients, personally, and used Azureus for a pretty long time until one of my friends nagged me into switching over.

Interestingly, on my dorm internet, where they have some sort of firewall or something set up to block a lot of P2P traffic, Azureus often worked better than uTorrent. But it also crashed my connection a lot more. If you are an open connection and will be able to connect normally, uTorrent should give you better speeds, and it's way less system-intensive.