Where you would notice a difference routing HD-DVD audio through a capable HMDI receiver verses what you are doing now (analogue), is bass management, channel adjust and post possessing within the receiver. Now, you have to adjust the channels with the DVD player and all of your bass management is also handled by the DVD player. Some receivers (very few), will allow you to control the LFE channel and post process DD EX / PL IIx or DTS ES to extract a sixth and / or seventh channel off the analogue inputs, but I doubt yours will do that.
When you go with a receiver that processes uncompressed PCM audio streams from HD and BR players, they will process this data stream the same as your current receiver will process compressed DD and DTS sound tracks that are also included in the high def disks.
Clear as mud?