I am looking to buy a new graphics card to run dual LCD monitors. I notice that quite a few cards only have one DVI and one VGA port.
Will I notice any difference in picture quality in a card that has two DVI ports vs one DVI and one VGA?
Short answer: yes, two DVI outputs is better.
VGA is analog. Since CRTs are all but extinct, VGA serves no real purpose these days. There are some very good reasons to choose VGA over DVI, but none of them are really pertinent for a home desktop computer. Using VGA means that you first have to convert the video signal to analog for transmission over the cable. Then, your LCD (presumably) monitor has to convert it back to digital. Usually this is done perfectly, but there is a chance that interference will cause degradation. With digital, it's basically an all or nothing affair. If you see something, the chance that it doesn't perfectly match what was intended is extremely low. DVI is a purely digital signal.
If you must use an analog signal, most graphics cards will allow you to use a DVI to VGA adapter. This is no worse than an output port that is VGA only.
Having said all that, will you actually be able to notice a difference? Probably not. But why chance it? If there are two cards using the same chip, and one has dual DVI and the other DVI and VGA, the latter is probably a lower quality card anyway. You're better off paying the extra money (if it even costs more) for the card with dual DVI.
I recently purchased a new desktop with a dual head. I went through a lot of VGA cards, and the clerk at the store insisted that DVI + VGA would just be fine. Long story short, he had me test two dozen DVI + AGP cards before conceding that I was right: The image is not the same on both plugs.
As I was using a DVI->VGA converter, I was using the exact same cable and monitor on both plugs, but the one on VGA was very slightly distorted. This would never have been a problem on a single screen, as your eyes would simply refocus. But having two screens, one very crisp, and one slightly distorted, eventually gave me severe headache.
I just got a DVI + DVI card in the end, and I've been very happy ever since.
YMMV, but I will never again bother with different plugs for dual head boxes. DVI + DVI is the way to go.