in short...
First, to clear away one element that can be confusing: DVI and HDMI are exactly the same as one another, image-quality-wise. The principal differences are that HDMI carries audio as well as video, and uses a different type of connector, but both use the same encoding scheme, and that's why a DVI source can be connected to an HDMI monitor, or vice versa, with a DVI/HDMI cable, with no intervening converter box.