What are the prices that you're looking at? The 7850 is a generally significantly superior card, but if the 560 Ti is enough for you and much cheaper, then there's little reason to spend more for something that is more than you're going for unless you have really bad electricity bills where the 7850's significantly lower power consumption is a big deal.
i would consider what games are involved; if you are looking at more recent titles then the 7850 would provide better satisfaction.
though if you are wanting games that are a few years old or playing at lower resolutions than 1920x1080 and medium settings then the 560ti would be fine. esp if it is much cheaper.
I'd say that the 560 Ti would be fine regardless of the game's age, although the 7850 would generally be better. Technically, if we went by older games, the 7850's advantage could grow because you'd have to use higher levels of AA and such to make use of its higher performance and it has extremely good AA and tessellation efficiency.
The 7850 is faster than any 560 Ti in almost every game at almost any settings. Without knowing the prices that you're comparing, I can't say if it's enough of an improvement to be worth the extra cost.