HD 7850 or GTX 560 ?

7850 straight away. Just got P6600 on 3DMark11 and 4100 on 3DMark FS. 1050/1300 clocks.

I'd rather spend the $35 for the i5 3570k than to go with the HD 7870 .

Oh OK you're the same guy from before haha. Yes if the 7870 is out of budget like I said before go with the 7850.

If possible go with a Radeon HD 7870 or else HD7850 2GB GDDR5 model

Isn't the memory just for high res gaming ?

Hello.
If you have already bought this system then I suggest you to go with 7850 2GB. The games that need more than 1GB VRAM at 1080p are increasing at a very fast rate. (Even skyrim on high settings with high res pack from bethesda lol.)

If you didnt already bought the system I have some suggestions to make.

This is a no-brainer, get the 7850.
It greatly outperforms even the 560 Ti.

This is a no-brainer, get the 7850.
It greatly outperforms even the 560 Ti.

I haven't bought this system . Please don't give me suggestions with rebates . My budget is around $600 .

get 1600 mhz ram

Yes you are right the truth is if you are gaming at 1080p or higher 1GB is a bit low now. Latest games like BF3, MaxPayne 3 on my HD 5770 1GB is really tight. So if you are gaming on a much lower resolutions like 1366 x 768 then 1GB version is still sufficient. If you gonna game @ 1080p or higher go with the 2GB GDDR5 to be on the safer side..........