The 480 does run hot in comparison to the 5870 and it certainly does use a lot more power.
More power means more expensive to run. It depends on who pays the power bill at your house.
It also needs a good quality PSU. At a guess, I'd say your current PSU may not be up to scratch.
It is more powerful than than the 5870 and nvidia drivers
are arguably better than ATI.
The 5870 does run cooler and uses a lot less power.
At your resolution, the 470 is also a good alternative.
If you can afford to wait a little bit longer, the 470's replacement is reportedly more powerful, runs cooler and uses less power than the 470 and is due relatively soon.