I have an ancient Dell Dimension 5100 that requires a half-height card. Aside from the heat issue, the 4870 looks like the way to go, even though it's got half the memory of the 5670. I feel like my 350w PSU will still power either one of these, based on what I've read, but it does currently power 2 250gb HDDs and a DVD-RW.
With the limited space in the case, I guess the heat benchmark on the 4870 is what concerns me the most. Trying not to have to go the aftermarket cooler route.
performance wise 4870 will eat 5670 for breakfast though it does not have dx11. i think 4870 is more comparable to moderately overclocked 5770/6770 (stock 5770/6770 is a bit slower than 4870). you can power 5670 with your current PSU but not 4870. AMD themselves recommend 500w PSU for 4870.
btw how much you can get for both card? i think it is better for you to get 5770 or 6770 since these card perform almost the same as 4870, use less power and have dx11. (but you still need new psu for 5770/6770)