Well It's a pretty new card... so maby the drivers aren't very compatible with certain games at the moment? GTA 4 is also a terrible port to the pc... I benchmarked at 60fps but got 5-20fps in game with allot of stuttering.
I have also got a 7870, but I had 2 GTX460s in SLI - the performance has INCREASED. It tops a GTX580.
I love my 7870 - It runs Metro 2033 on Very High with DoF at playable fps. Although I have had some serious issues overclocking it, its happily overclocked now @ Stock volts. I'm pushing more out of it when I download the new Sapphire Trixx tonight.
To OP - you need to check that the clocks of the 7870 and its temperture are fine, and the card's usage is 100% on the stress test.
Maybe there are some left-overs from the former Nvidia drivers. Try to run a driver cleaning software on safe mode and after that install the 7870's drivers.