The question is, why do you want to upgrade from an S3 to a Note II? The Note II does have a larger screen, s-pen and multi-view. If you wanted to upgrade for example because of the larger screen, then you can't really go wrong with the Note II. If you just want to have the latest and greatest phone, really, my S3 and Note II run about the same, save the 3 points above.
And what is important to you? For example, the DNA has 200% the number of pixels as the Note II, on a substantially smaller screen, and it has wireless charging. If the highest pixel density is important to you, then for you, the DNA may be the best phone out there.
Really, only you can decide what is the best phone, and whether or not it's worth it to upgrade. But, IMO, don't just get the Note II just because it is the latest and greatest, get it because it provides some improvement to you.
Sent from my Verizon Galaxy Note II