Thank you for the clarifying the difference. Does the amount of VRAM that a card has affect performance greater in 3D work/scientific calculations or gaming? The 670 seems better for gaming, and worse for double precision operations yet has a larger VRAM, whereas the 580 is better for double precision operations and worse at gaming yet smaller in VRAM. Only by 0.5GBs albeit. Do you think that is anything to cry over?
The performance difference in the amount of memory between the two cards is probably not significant. It's the architecture of the GPU and the memory bandwidth that really affect things.
Generally speaking, extra ram on a graphics card (past that on stock cards) is essentially useless. There are some edge conditions where it does provide an advantage (such as very high levels of anti-aliasing at a very high resolution), but typically, if you are using a card for tasks where the extra ram would provide a significant advantage, you are probably pushing it beyond what it is really intended to operate at.
After all if 2 x RAM did provide for some substantial boost, 2 x RAM would be the stock memory amount. nVidia and AMD don't pick the amount of ram they have on the cards at random after all. In general, the amount of ram is going to be some multiple of the width of the memory bus and this is one of the main reasons why doubling or tripling the ram has limited effects at best.
Video cards need to shove ENORMOUS amounts of data into the GPU and back into their memory, so how wide that pipe is between the GPU and the on card ram, has a major effect on how much memory you can really use. Since it does you no good to have the ram if you can't push the data through it quickly enough to be of use. When you double the ram, the width of the memory bus is not increased. So you don't get better performance. In fact, one of the main ways you'll see them artificially create differences between graphics cards with essentially the same GPU chip is to restrict the width of the memory bus on the lower end card or sometimes they will use a ram with a lower throughput like GDDR3 vs GDDR5.
Now there are a few caveats to that, depending on the software and possibly even the specific application.
If what you are doing directly uses the ram on the card, say for storing texture information in a 3d app that processes the texture data on the card, having more memory directly and quickly accessible will result in an improvement vs having to fetch that data from the computer. This can be a major improvement if the application uses this properly and it is the correct kind of data. GPUs tend to be great at highly parallel tasks, since that is essentially what they are designed to do with 3D games.
This sort of improvement tends to be highly specific to individual applications and can be wildly affected by the specific architecture of the graphics card as we see with the double precision math on the 5XX vs 6XX nVidia cards. However, it is one of the reasons why some of the high end "pro" cards like the Quadros or FirePros can have as much as 12gb of ram (those cards do cost an arm, a leg, a kidney, a pancreas....).
On a non-"pro" card, they stick extra ram on the cards mostly because people don't always know the difference between individual GPU chips or architectures, but they do understand that 4 > 2. So hey that 4gb 630 has to be better than that 2gb 680 right?
