I have heard that some video editing programs work better with Nvidia. Not sure which ones - does anybody have a round up of popular programs, perhaps? Some video editing programs seem to utilize graphical memory, others do not. Others say CUDA, and some even say an AMD 5750 has plenty of horsepower.
KueB, it would be worth a google on your software brand to see what other users have experienced.
Adobe, in particular, certifies their products for use with NVidia graphics cards - specifically the GTX 470 and more expensive workstation cards, but most other flavors of these cards can be modified very easily to fully support CUDA (on the drivers side of things).
Tom's Hardware does their CS5 testing on a GTX 480 system: http://www.tomshardware.com/reviews/adobe-cs5-cuda-64-b...
If you are not using Adobe products, then it certainly would be a good idea to google search your intended software and find out what other users recommend, per eloric's recommendation.
And none of my input is intended to downplay the potential that a Radeon 6870 may have ;0)