Between the same generation of cards, if they use the same type of memory, the card with the higher bus width is faster.Otherwise, it doesn't really matter, as long as you're comparing cards which have the same horsepower, and choose cards which don't a very big generation gap.
For example, a HD 5750 128 bit GDDR5 is as fast as a HD 4850 256 bit GDDR3.
The size of the bus is basically how many bits can be read in one memory read. If you have half the bus size (128 as opposed to 256), you need to read at twice the speed to pull the same amount of data in the same amount of time.
Classic architecture argument: large bus with slower reads, or smaller bus with quicker reads.
Wondering how much improvement I'll notice in a 256-bit vs. a 128-bit bus width on a vid card.
Pretty much faster speeds lower bus or bigger bus slower speeds..I bought a gtx 660ti around launch and dont get me wrong its a great card but for price per formance i should of went for the 670 due to the 660ti has been gimped..I see why people now actually warned me to sorta stay away from the 660ti but i read in to late after purchase..NEVER AGAIN