Firstly, congrats on your psu, its a great choice(its the one where the gx is writen in orangei think) anyway that is a single rail psu, so you have enough "juice" for any single card, I ran a stock 580 with a gx650 psu and even overclocked my i7 950 at that stage, so no worries in psu. As for comparrison, I am not gonna post stocks,and graphs and all that stuff, I will keep it simple.
480 was the best 4series card.
580 destroys a 480 in any game/bench test.
Some test and most games, a 570 will beat a 480.
A 560ti is weaker and performs much less then an 580,but uses less power and stays in the 50-60degrees C, the 580 will EASILY reach 85+ degrees C if you dont have effective cooling.
The 560 is newer tech then the 480, but 480 is more powerfull. Mostly users will get a _70 cause its a great value for money, ie: 470 or 570, the 570 uses less power and has less heat then a 580, and performs a little less, on extreme games,it will perform even less than a 580, but is still better then a 480 or 560.
Basically, 680 better then 580, 670 sometimes better then 580, 580 better then 480,470 and so on. 570 better then 480,470... And lastly 560 cheaper then all, and good power/performance ratio. But if you want to wait, then opt for a 580,from personall experience they are beasts! Then again, a 680 is better.
Edit. Please update your system specs in the left corner, for example,look at mine, it must show atleast the basic details, so we know what chassis you have,size ect.
As for if it will fit, yeah aslong as your mobo supports x16 lane(not realy,just aslong as it has a pci slo

) and if your mobo is an atx form factor, then it will give you a good basis, a 480 is maybe a little longer then a atx board is wide, 580 sticks out a bit more.