Mac – Rainbow display static/snow over HDMI->DVI

Modern digital displays (like LCDs) that use DVI use the DVI-D flavor. That means there are no pins above and below the blade. The included HDMI-to-DVI is DVI-D, so that it can plug into such monitors (or monitor extension cables). If it were to-DVI-I, it would not fit because there are no sockets for the pins around the blade on many/most digital displays.

To convert DVI to VGA, the other end has to be either DVI-A or DVI-I, because those are the only two that carry the analog signals. Once you have used an HDMI-to-DVI-D adapter, those DVI-to-VGA adapters won't work.

Furthermore, there are no simple HDMI-to-DVI-A (or -I) cables/adapters, because they are not directly compatible. HDMI does not carry an analog signal. You need an active converter; HDMI-to-VGA converters exist, but are in the $100 range.

I've never seen a DisplayPort to DVI-I adapter. Even if such a thing existed, you might as well skip the extra conversion step and get a Mini DisplayPort to VGA adapter. Not necessarily the $29 one made by Apple, although it might be more likely to "Just Work".

The only benefit to HDMI is that you don't need a second cable for audio. HDMI essentially combines a DVI connection with audio. Actually, because of this, you can acutally get converters that go from HDMI to DVI for a few bucks.

Because it already has a DVI connection in it, the quality over the HDMI connection would be identical. The only reason you'd want to use HDMI is if you'd like to run sound through the monitor--but it's not going to improve the video quality.

That being said, there's a ton of other factors that affect "video quality". Variations in display coatings, backlights, and LCD panels can make the same "red" icon look very, very different on two different displays. However, since DVI and HDMI use the same digital link, there's effectively no signal loss, so one wouldn't look any different than the other on the same display.