I am upgrading my computer, but am unsure which component is more important for HD video editing. For the same price, one computer has 9GB memory and a 1.8GB video card, while the other has 12GB memory and a 1GB video card. All other specs (and make/model) remain equal. Which would be of greater value from an wedding-editing standpoint?

Michael, may I suggest you check with the maker of your editing software as well as checking with other users here. In my experience the spec is much likely to be driven by the software designer than a users experience. They may even publish ideal/minimum specs.

Only then should the way you work and the need for specific features eg a render farm come into play.

Both systems you're considering far exceed the recommended specs for Adobe Premiere/AE and Sony Vegas.

Which video card you get depends more on the chipset than the RAM. For example, Adobe supports eight NVIDIA graphics cards (http://www.adobe.com/products/premiere/systemreqs/) for GPU acceleration. If it's not one of those cards, it wouldn't matter if you have 1GB of VRAM or 64GB.

Tell us what software you're running and the make/model of the video card choices and you'll get better advice.

I'm actually considering switching from Mac to PC, so I'd be using Adobe. One is a 1.8GB nVidia GeForce GTX 260, and the other 1GB GeForce GT220. Doesn't look like either are GPU accelerated.

Go with gtx260. Adobe CS5 will be able to use the graphic card to accelerate the live previews.