I have a friend that uses the GS3 and I picked up the Note II 3 weeks ago. We've run comparisons (On T-Mobile 4G) and the Note II is slightly faster with all applications. Mostly due to the quad core processor vs the dual core of the S3. Now, the difference isn't marginal so it's not a deal breaker.
The screen size of the Note II is awesome for me. I'm a tall guy with long fingers and texting on small screens is horrendous. The Note II offers the best screen for me since I prefer texting and it's the perfect size. When I first got the Note II it seemed so big because I wasn't used to it. However, after the few weeks of having it, it seemed normal. Now when I see my Girlfriends iPhone... i can't believe how small it is. It really puts smaller phones into perspective.
In the long run, these phones are almost identical in features. The note II has a few extras that I particularly enjoy. The S-Pen really comes in handy as it doesn't have to touch the screen. It helps highlight and select options much easier. It also has a scroll over effect in many applications that allow you to see more before a selection, much like the mouseover effect on a PC. The screen size is larger and the processor is a bit more powerful. All in all, both phones are great. Size and functionality are what you'll need to decide. As other mentioned, play with some at a store and get a feel for what fits your hand and functionality better.
Good luck and enjoy your new Samsung phone