yeah, I just got it running today. 2x5970 + 1 6870 on Linux.
The 6870 will not work with ati stream sdk 2.1, you need to upgrade it to the latest AMD APP SDK2.4 .
So far i've had the best performance from 2.1. So i'd recommend using 2.1 for everything that it works for, and use 2.4 for the newer 6X cards.
To use both 2.1/2.4 you add both paths to your LD_LIBRARY_PATH, i.e. make sure you have the path to 2.1 and 2.4 libs in there. If you do this, the miner, ex phoenix, will see this as a second platform. SO you can use 2.1 for your older 5XXX cards and 2.4 for the newer 6XXX cards. 2.1 was the fastest for me for my 5970s, so I'd recommend 2.1 for everything, and if that doesn't work, use the 2.4.
make sure u specify the PLATFORM=0 or PLATFORM=1 when accessing the different versions of the sdk.