Performance on the Note was great, I pushed it with my usual multi-tasking, where I'd be running applications over the entire day and it never broke a sweat. The included 1.4GHz dual-core processor cranks along without hesitation. I would go in-between e-mail, social networking, surfing the web, snapping photos and it never missed a beat. Performance is something you truly don't need to worry about on the Galaxy Note.
Toward the end of my use of the Note, I began to notice the smartphone would slow down and almost crash with certainty in certain apps, such as Google's own Chrome browser. I found if I had 4-5 tabs open and tried to access one of those tabs after an extended period of time (4-6 hours or more) then it would either lock up the app and I'd have to force close it or I'd have to fully reboot the Note. I never experienced this with my Galaxy S II.
Other than that Chrome-related hiccup, the Note ran admirably. If you've ever handled an S II, the Note is virtually identical in terms of performance, multi-tasking and general use.
3G performance on the Note was impressive, where in the middle of the CBD of my home city (Adelaide, South Australia) I received a downstream speed of a little under 13Mbit and an upload speed of just under 1Mbps. Other tests saw down speeds of 9Mbps and upload of 2.5Mbps.
Battery life on the Note was surprising; I used the phone moderately during the day and more heavily during the night. I had the screen on automatic brightness, every now and again changing it to full brightness if I was watching a video or playing a game.
I was able to get through an entire day most days without needing to charge it, which is an impressive feat considering the device is powering a 5.3-inch screen.