about graffic cards

Solution
When picking between two of the same model of card that offer a 1GB and 2GB version, 99 times out of 100 you should be going with the 1GB version. Reason is, it will be GDDR5 (faster memory) as opposed to GDDR3 (slower memory) that is usually on low end 2GB cards, but of-course there are exceptions (7850 for example).

The stat refers to the framebuffer, how much stuff the card can store, capacity doesn't affect performance until it fills up. Which cards are you picking between?
When picking between two of the same model of card that offer a 1GB and 2GB version, 99 times out of 100 you should be going with the 1GB version. Reason is, it will be GDDR5 (faster memory) as opposed to GDDR3 (slower memory) that is usually on low end 2GB cards, but of-course there are exceptions (7850 for example).

The stat refers to the framebuffer, how much stuff the card can store, capacity doesn't affect performance until it fills up. Which cards are you picking between?
 
Solution
given that all other things are equal, the 2gb is better.
the answer to your question is already stated above (the frame buffer), just remember that having 2gb does not mean it is faster/better than the other 1gb card. A good 1gb card will wipe crush the 2gb model if the 2gb is a cheap/slow one