At the low and midrange ends, the AMD cards are a much better deal. At the mid-high and high ends, it is debatable, and tends to switch back and forth. This difference comes down to the way they design their chips. Nvidia builds very complex high-end GPUs for their "halo" products, and then cuts them down for the mid-upper range parts. This means that the low-end and solid middle-range cards, tend to be last year's stuff relabeled, because they haven't actually designed anything specifically for that product segment. They basically count on the "halo effect" of their high-end parts, to trickle down into their midrange and low-end parts (people think that because the high end card rules, that their $150 card must be good too). Quite often, when you look into it, their low/midrange parts are a whole generation (or sometimes two) behind.
AMD designs their GPUs solidly for the midrange price point, and then scales down from there (using the "double GPU" cards for their high-end, with no giant monolithic high-end GPU). This largely cedes the single-GPU high end to Nvidia, but it makes them VERY competitive in the middle and low-end of the market. I find that AMD tends to have better HDMI support, better hardware deinterlacing, and I actually like their drivers MUCH better than Nvidia's (now, this was NOT always the case). I think that often their "features" are better than Nvidia at the low/midrange because of their different design philosophy. When you buy a midrange AMD GPU it is usually actually a current generation chip, which means you get things like HDMI 1.4 and DTS-MA bitstreaming support (the 6770, which is mostly a rebadged 5770, notwithstanding). Nvidia tends to "rebrand" their low/midrange GPUs from last year's high end. This means that, while the top chips from Nvidia will have those features, it usually takes another cycle before they trickle down to the midrange.
On the other hand, Nvidia often tends to have better third-party software support for things like GPU acceleration of video decoding and special features in games. They throw lots of money at those problems.
If it were me? I'd probably get a 6870 or 6850 if you don't really care about 3D gaming performance at all. If I was looking the next "step" up (the 6950 vs the GTS 560 Ti), then it would be a lot closer of a call, and I'd have to look at individual cards and packages to decide.
If all you care about is GPU acceleration of H264 video, because your processor is crap? Then probably go Nvidia for now (though you could just try CoreAVC for $10).