Your GTX560ti is already a very good card.
You need to jump a couple of tiers in capability, or you may be disappointed if you do not see a big improvement.
See if you can't find a GTX670 or 7950 on sale at your price point.
You can sell the GTX560ti to recoup some funds.
The GTX660ti is a notch below depending on the game. But, I would not put much import on bandwidth spec issues, or any others for that matter.
Engineers balance the specs to achieve a desired price/performance level. How they do it is of no great importance to us amateurs.
Honestly, having a 560Ti/2500K combo right now myself, I don't see much of a dramatic upgrade for you in the <$300 range. I wouldn't consider upgrading mine for less than a GTX 670/7970. (maybe a good deal on a factory-OC'd 7950)
The 660Ti is designed for 1080p and below... its memory bandiwdth seems plenty for that purpose.
As long as you game at 1080p or below, the 560Ti does quite well.
Sure, a 660Ti would be faster... but is it $300 faster?
Not in my humble opinion. (in the games I play)