Comes down to screen size really. I had both, AT&T S2 and I now have the international Galaxy Note. I loved both, but the Galaxy note is my favorite phone of ALL time! The 5.3 inch HD screen is ABSOLUTELY GORGEOUS! The 4.3 inch on the S2 is very nice as well with a resolution of 480x800.
Speed: Both are very fast, very fast. I really can't say if one is really faster...1.2 dual core exynos vs 1.4 dual core exynos. One pushes a smaller screen, one pushes a lot more real estate. Speed I would say is a tie.
Battery:A BIG thing for most people. Both last ALL DAY no problem for me. I usually use average data. At home with just A LOT of texts, some browsing, games I normally have 70% after 10 hours or so. Both battery life is great on these devices. Tie
Price: Depends on how you look at it, GS2 will be cheaper, its an older phone, simple as that. $200(Might be less nowadays...haven't looked) vs $300 but those prices are on contract on AT&T. I paid full price for my Note...so 7 big ones...but def worth every penny in my eyes. Tie IMO.
Media: Same player, speakers are about the same, video is WAY better on the Note, hands down. Note is the clear winner.
Camera: Tie....same exact camera and sensors I am pretty sure. Just the CPU is the big difference(which really isn't much)
Texting: This is all based on your preferences. I like the Note texting a little better. Larger is better for me haha. I am a rapid texter. Tie
Updates: AT&T will always be late...normally really late. International versions get them first(which is a great plus for my note). Both will be seeing Ice Cream Sandwich which will be a great upgrade for both phones.
I hope this long explanation/breakdown somewhat helped you. Everyone has their own preferences.... For me, the Note is the winner for me...
Long as you don't wear tight jeans...the note fits in your pocket perfectly fine. They do mine, haha.