I have one from MSI, and i can tell you it is very good, great for gaming at 1080p, also a cheap solution if you wan't to go for SLI in the future, the 560 ti SLI scaling is very good someting like "560 ti + 560 ti = 585" that is what they call lol...
If you are an amd fan you can also go for 6950 (normally used to comparisons agains 560 ti), great card also.
well nowdays you have the option to go for a 560 ti 448 core what is really good, better performance than a 570 but the price is also higher.
For the price, and the performance, i am really enjoying the 560 ti, and i know that when i need more firepower, i can go for sli buying another.
Generally it is a very good card. But it competes with the 6950 1gb, and that one is often a little bit better price/performance.
In terms of raw performance the two are very close. I guess it kind of depends on the games you play, as Nvidia likes to buy off more games (Nvidia's "The Way It's Meant To Be Played") and there are some reports that they purposely code games to run poorly with AMD hardware (even though it could run better on both cards if they just optimized properly).
But that's neither here nor there. The point is, it's a good card, the competition is the 6950 1gb, and you should just check reviews on the cards and look at the games you are currently interested in playing to see which card generally performs better for your tastes. Either one will serve you fine in the end.
I do not have the Ti model, but I do have a GTX 560. It runs BF3 and Arkham City very well - and thus runs pretty much everything else extremely well.
As personal preference I do keep the case open and an external fan on it as (for me) it tends to overheat and freeze the computer - especially when I forget to turn my fan on.
I have not looked at the specs for many other cards, but you could go back to a car about half the price and get 2 of them. SLI-ing 2 much cheaper cards will most likely give you the same power as a single 560. The downside is that you could also - later - SLI 2 x GTX 560s and be covered for years of gaming.
On the other side - you could also look into a higher end of the 6000 or 7000 series of Radeon HD cards.