The Note 2 is an overall better device than the SIII. Bigger battery, faster processor, more RAM, everything. Except that one of its best features is also the worst: The big screen. It could be too big for some.
However I don't think the difference will be so much that it will be noticeable. The best things you'd additionally get would be the S-Pen support. Basically just a better stylus than whatever you can have anywhere. The special features like AirView and Multi-Window is coming to the SIII in an update.