Samsung's two flagship mobile phones, the Galaxy S3 and the Note 2 both have 1280x720 HD Super AMOLED displays, but they are quite different: the S3 uses a Pentile sub-pixel architecture while the Note 2 has a unique RGB matrix. AndroidAuthority posted an interesting article comparing these two displays from a user point of view.
The conclusion? Both displays are excellent, and most users would never tell the difference. The Note 2 doesn't suffer from the Pentile pattern (which is only really visible when you magnify the images) or the the slight greenish or bluish cast of the S3. They have a good suggestion - simply spend a few minutes with both devices and decide for yourself.
If you do want some technical advice, check out DisplayMate's iPhone 5 vs S3 comparison, and their Galaxy range shootout. Maybe they will publish their own Note 2 vs S3 comparison soon.