When you say some graphics cards you need to be a little more specific because there are two major gpu manufacturers and they do support different features along with both supporting some of the same. An example is that AMD has Eyefinity which is a nice feature where you can have up to five monitors and your desktop stretched out over the five. Naturaly this requires some more memory and you can see that a lot if not most of the more recent cards have at least 2gb of ram. Nvidia on the other hand does not have Eyfinity they have 3d vision which is only 3 monitors so you have less ram. The memory on the video card is only for that video card to use and is only one part of the card but sometimes people see that and think this card is better because it has more ram when it is only better if you are going to use that ram for your specific setup.
The main components of the video card that make a defference is the gpu, the number of core processors , stream processors , shaders and the memory bandwidth which is the 128 bit 256 bit , 384 bit and 512 bit. For example Nvidia just released a new GTX 560Ti card that has 448 core processors , where a normal 560Ti has 384 , and this will add to the performance of the video card.
In the end the best way for you to determine what card is best for you is to look at a lot of different benchmarks done by different sites (like this one) and see what is best for you. There will always be brand wars and you can take advantage of that by snaging a good card on sale because of the competition , but you have to do your homework so you will be ready.