I don't think I'd use the 5770 because I heard it doesn't provide stable fps when playing on resolutions like 1920 x 1080 (my native). I don't think I mind purchasing a new power supply if the 260 is my only option when it comes to getting +60 fps at 1920 x 1080.
The GTX 260 is less than 10% faster and the 5770 overclocks a lot better so it will end up faster anyway if you overclock.
EDIT: I heard ATI drivers were incredibly buggy as opposed to nVidia's. Also, can I run a 450w card with my 350w PSU?
They lied, the drivers are the same.
What do you mean ' just get a new power supply'? In case I go with the 260?
To be honest, I'd rather get a card that'll work with my current PSU as I don't want to go through the troubles of emptying my wallet and wasting my time to replace it.
No, but you can power this:http://www.newegg.com/Product/Product.aspx?Item=N82E16814150485&cm_re=5570-_-14-150-485-_-Product
Look at the graph above.