It depends on a few things, if you are gaming over a resolution of 1920x1080 you will probably benefit from the extra memory.
If your monitors resolution is at 1920x1080 or under, the 2GB of memory will not be put to full use.
The Ti version is a better/faster card then the standard 560, but not by a huge amount.
The Ti card can run BF3 on a high settings for me with a frame rate of about 50-70FPS
I play at a 1920x1080 resolution with a 1GB 560Ti card.