Purely speaking image quality, HDMI is the same as DVI, it's just a different connector. You can buy adapter cables from one to the other if necessary.
BUT ... DVI does not have audio or anything else, it only transfers the image. I don't know if Playstations have a separate cable for audio?
The 2412 is a great monitor for the price. Only sometimes the backlight can have some bleeding in the corner.
If you want the best for gaming there is the popular Asus VG278HE, but i haven't seen what the difference is myself.
You could also probably get a big ass television for the same price.