Honestly, most of the standard video editing applications on the market (like, Adobe Premiere Pro) have optimizations for nVidia's CUDA GPGPU technology. Nobody uses AMD cards for video editing. As far as gaming goes, they're extremely competitive, but for video, it's a much better plan to use nVidia.
Additionally, video RAM isn't the biggest consideration when editing video. texture fill performance generally correlates to GPGPU performance, which is a better indicator of accelerated video editing performance.
I suggest you look in to a GeForce 460. They're about the price of the (rather antique) cards you listed, and you can (with the help of an edited text configuration file) enable it to do CUDA acceleration in Premiere Pro, etc. The 460 is roughly equivalent to a Radeon 6790, and they're about $125 right now on the egg.
Just caught your edit. I'm assuming you're talking about video encoding or transcoding when you talk about video "rendering" The advice above as far as CUDA is concerned still applies. there are many more nVidia aware GPGPU applications at the moment.