If you're in North America, Note 2, if you're in Europe, Galaxy S3. Note 2 is dual core same with S3 in NA, and S3 is quad core in EU.
-LeetNeo.
Just to correct, the Galaxy Note II is a quad-core in North America, South America, Europe, Africa, Asia!
The difference between the Galaxy SIII and the Galaxy Note II is that the Galaxy Note has a Cortex-A9 based processor, the Galaxy S3 has the same Cortex-A9, but in the US, it has a dual-core 1.5GHz Snapdragon which is based on Cortex-A15.
I would personally go with the Note! It's better in everything!
-Decent battery.
-Decent processor.
-Awesome screen & resolution, 1280x720!
-2GB RAM.
-Stock Jelly Bean.
The S3 is decent, too. But, if you're going with a big-screen phone, (I do realize that the Note II is a Phablet) Go with the Note.. HTC phones are really decent and pro, too. For example, the Droid DNA, a 1080P (The only one in the world) display (1920x1080) Pro camera and a Quad-core clocked something like 1.7 or so..
Anyways you can watch reviews on Youtube to decide..