I've had the Note for awhile. I initially thought that my battery was alot better in the S3, but once I got everything setup, and all the same apps installed, its about the same for me.
I'm not a benchmark junky. All the games were smooth on the Note, and are equally smooth on the S3. Where games tended to hang or lag, they pretty much do it on the S3 too. Like Mini Motor for example. There's no denying the S3 is faster and has more ram. The S3 has higher resolution. faster cam (although not seeing a big jump in quality). But in real world use, they are both very good and in my opinion comparable. Of course there are tons of neat things the S3 can do that the Note cant, but in daily use, it's hard to quantify the value of those features. At least for me. Other people may use Photo Buddy Share every day. lol
The Note just has such a huge advantage on useability. The screen real estate is just so awesome. Typing is easier. browsing is more comfortable. The wider aspect ratio screen is just so much better in so many apps. I *love* the Note. It's huge for a phone.. but small for a tablet/pc that you can have with you at all times, right? However, it's size just finally got too tedious for me. I'm enjoying the S3 right now, nice to have a reasonably sized phone that can be handled with one hand. I can do much of what the Note can.. so, I'm going to stick with the S3.