Carl, first off, I think when you refer to DVI-I, you're thinking more of DVI-A, which is the spec for analog signals in a DVI connector; DVI-I specifies both analog and digital over one line. Most computers with DVI-I outputs support both signal types; the card detects what type of monitor is attached and enables the appropriate signal.
Now that said... you SHOULDN'T see a difference between DVI-A and VGA, because DVI-A carries the same analog signal as VGA. That's why adapters are cheap - they're just pin-to-pin adapters.
Similarly, you shouldn't see a difference between DVI-D and HDMI, since HDMI's video signal is the basically the same as DVI's; HDMI merely adds digital audio, extra video modes, control signals, and other data (latest spec even rolls in TCP/IP). And as such, DVI-D/HDMI adapters are pretty much pin-to-pin as well.
If you want to see the difference, put an actual DVI-D or HDMI monitor beside a VGA monitor, running off the same machine. Even with a good quality cable and set at the proper native resolution, the VGA will often show a "softness" to the picture. It's often not even noticeable until you have the two side-by-side.
All that aside, if DVI is "dying off" it's probably mostly because HDMI offers the same signal and compatibility, but in a more consumer-friendly form. The additional data HDMI carries won't be applicable in a lot of computer applications, but are in multimedia, home theater, etc., so it makes more sense to build displays, receivers, and other non-computer gear to accept HDMI, since they can still accept the DVI image. HDMI has the added "benefit" of a smaller connector, which allows for much higher density - a four-head HDMI card can fit in a PC backplane in the same space as only two DVI connectors. In short, DVI is simply being obsoleted by HDMI.
As for VGA... I certainly hope it's not going away anytime soon. It's far more flexible and versatile for computer/surveillance purposes. VGA is easy to extend several hundred feet over (relatively) low-cost baluns and KVM extenders; DVI and HDMI typically require expensive converters to do the same thing. If you need to output a VMS to multiple remote monitors, VGA can be substantially less expensive.