The GPU will make the most difference. RAM won't make a huge difference unless you have a very small amount of it eg. 2GB. If you have a very low amount of RAM, the game has to go to the hard drive to grab data, and that will hurt performance a lot.
As for RAM on the video card, for some games having more than 1GB will make a difference, especially on higher resolutions with lots of AA and/or if the game has high resolution texture packs. For a card in the class of the 7770 though, it generally is not worthwhile to get the 2GB version, as the 7770 isn't fast enough to really take advantage of more than 1GB of video memory. For the 7850 on up, you definitely do want to have at least 2GB of video memory now, as lot of games have been coming out with high resolution texture packs lately, and 1GB of video memory isn't enough for those high res textures if you are trying to run a game at 1080p.