I built my system last week using this Geforce GTX 670 which seems to have more memory than your average 670 (4GB vs 2GB). My friend recommended I use EVGA's step up program to upgrade to this 770 which, while being a 770, is down to the 2 GB of RAM.
Am I getting an overall better card for gaming by using the 770 w/ 2 GB instead of the 670 with 4? What exactly does memory do for a card?
More about :important memory graphics card regard performance
memory ammount is important for games that require more storage for visual images including post processing effects, but generally does not affect performance. What affects memory performance is the speed and bus width of the memory, as both combined decide the max amount of data that can travel through, where if its too slow(or clogged up) it hinders performance. Generally its better to get the 770 with 2gb for best performance, unless the majority of games you play happen to use more than 2gb of vram
Having 2GB of VRAM will suit you just fine playing anything on ultra in the case of the GTX770 1080p. Getting let's say the 4GB windforce 3x Edition http://www.newegg.com/Product/Product.aspx?Item=N82E168... will be considerably better for a 3 monitor setup.
The CUDA cores help a lot. To understand this better, lemme explain something.
This example is a little on the oversimplified side, but it should give you enough to get started. After which, I'd suggest some of the fine articles on sites like Tom's to get more of the specifics.
If you think of your video card like a freeway, then CUDA cores would be analogous to the number of lanes in the road, clock speed would be the speed limit, and memory interface would be the number of lanes for exit/entry ramps. More lanes means more cars can be moving on the freeway at any given time, the higher the speed limit the faster any given car is moving, and then if there's say 2 exit lanes instead of 1, you can have more cars getting off the freeway, same as you can have more cars coming onto the freeway if there are say 2 entry lanes instead of 1.
Again, it's a bit of an oversimplified example, but it should be enough to get you started in understanding some of the articles explaining these things in greater detail.
In the end, the specs are irrelevant. What is important is game performance so you ignore the spec sheet and look at game benchmarks when choosing a card.
Now it's not to say that some games like Crysis 3 Might benefit of that extra 2GB of VRAM, (cuz it will), but if you're planning on gaming on an 1080p resolution only, no 3 monitor setup, 2GB will do just fine.
EDIT: Also, I should note that the GTX 770 model outperformes the 670, it being in the 700 series and having those amazing specs. Not only that, but it's a little bit cheaper, so I think IMHO that it would be the better choice. http://gpuboss.com/gpus/GeForce-GTX-770-vs-GeForce-GTX-...
Then if you want to future upgrade, just SLI with another 2GB GTX 770 and you get 40% more performance than a GTX TITAN, which should say something considering the price to performance ratio.