I had the Note and loved it. The S3 is about half an inch wider, and about 3/8's taller.
The only reason to get the Note over the S3 is the s-pen. The phone has some lag, but nothing unbearable, but it is about 8 months old now, and by tech standards it's old. The battery life was not great, but it was not bad either. I loved this phone. It was great size and the ability to take notes, and make notes on pictures was really cool! But it had it's drawbacks, and some just bothered me too much....for instance watching movies and/or videos it had trouble handling dark shades, and they would all look just washed out. The camera took amazing pictures, reading books, or the web was a pleasure.
The S3 on the other hand, has a gorgeous screen.. I got the chance to see it in person and it was just amazing. The battery life on any ICS device should be pretty good. My experience on old phones running ICS ROMs always had a great improvement on battery life. The thing the S3 brings is a better, more efficient chipset, a super fast camera with continous shooting and nearly instantaneous focus. It too has removable battery and can support up to 64GB SD Card.
I am getting my SGS3 Tomorrow, and I think I will not miss the Note much over it. I do have to say the s-pen absolutely made the Note an awesome phone, more than the screen and any of the other features...That I still miss. In fact, planning on getting the Galaxy Note 10.1 when it comes out. That will be the greatest device!
I hope this helps you decision.