I went from the GS3 to the Note 2 and haven't had a hint of regret. The GS3 feels tiny now when I see my friends. Once you get used to the size of the Note 2, which didn't take me more than a day, it's a win/win over the GS3. The Note 2 is faster, which is very noticeable in some of the more demanding live wallpapers and games, and it never jitters or lags. I noticed some homescreen to homescreen lag on the GS3, even after the JB update, but have never seen that on the Note 2. I personally don't use the S pen that much, but that's a matter of preference.
I don't like screen protectors either, they take away from the image quality and the feel, and I haven't had one on either my Epic 4G Touch, my GS3 or the Note 2. For the Note 2, I did for the first time since my Evo 3d, get a case. I picked the Seidio Active Case with Holster. To me the phone is too big to put into my jeans, and with the Active Case installed, the problem is multiplied by not only the added size but also by the silicones affinity for lint. The holster is sturdy and doesn't get in the way while driving either one of my cars. I love the kickstand, it comes in handy for watching any type of video content.
The big question for you now is whether you want to get the Note 2 still or wait for the GS4. I don't know if you have any upgrades available or if you buy your phones full price, but with some sort of announcement of the GS4 just a few months away you might just stick with the GS3. I have an upgrade available on April 1, so I am good to go whether I decide to get the GS4 or wait for the (in my opinion) inevitable Note 3. I am pretty sure both phones will have a 5 series Exynos A15 processor with a 600 series Mali GPU and a 1080p display, and if you do use an upgrade to get the Note 2, you will suffer from some buyers remorse a couple of months later.
That said, yankeeusa summed it up nicely when he said that the Note 2 was a GS3 on steroids with a very handy S pen. I am amazed how much my handwriting using the S pen looks to my actual handwriting, it really is a marvelous device.
Good luck!