What model? The 560 needs 24 amps(recommended).
Do you plan to use SLI or crossfire in the future? Does your motherboard support 2 video cards? What model and brand is your motherboard. If it supports SLI buy the nvidia, if it supports crossfire buy 6870 if you want to use 2 video cards.
I don't know the performance of the non TI version right now. Did not get the chance to search or read anything about it. Basically it's a stripped down version of the TI model, much like the GTX460 1Gb and 768mb. This version only has 336 cores, while the GTX560 Ti version has 384 cores.
I would invest a little more and buy the ti model since the difference in price is not that big. This is 230$ with mail in rebate http://www.newegg.com/Product/Product.aspx?Item=N82E16814130604
500 Watt or greater power supply (Minimum recommended power supply with +12 Volt current rating of 30 Amps.)