It all depends on your preference.. G-Note 2 is more powerful and has more real estate, but it is a big phone over all. S3 is slightly less powerful, but it is smaller and easy to fit in your pocket.. So it is all down to your own preference, for me though, neither of them... I already have Galaxy Note, and don't see a point why should I upgrade as of now... Nope, SIII has a quad as well.. http://www.gsmarena.com/samsung_i9300_galaxy_s_iii-4238.php
note 2 is really big... so i would suggest s3... but it really depends on what you use it for and how...