Your confusion is totally just, mandar5. I presume you have to choose between more memory and more bit-width coz of budget constraints otherwise there's no point in getting confused over this, get the best of both worlds.
There is no clear answer to this question unless you specify a chipset but I'd recommend you to go for more memory based on the video games you wanna play. Also, keep in mind that the chipset of the GPU plays a more vital part than the memory or bit-width. So go for a new chipset if you are given a choice between, say, a card with the latest chipset w/ less memory and an old chipset w/ more memory.
Hope that helps. Good Luck.
PS: I bet almost everybody will have a different opinion on this so please edit your post and start a poll, that'll give you the quickest no-nonsense answer.