Well the difference is not vast but to me a final rendered track in 24/44.1 compared to 16/44.1 is hard to put in words. The bass on synth sounds is slightly fatter, warmer, has more decay. There seems to be more 'air' around all the sounds with a slightly more 'open' spacious sound. I hate using cliche's but I cannot think of any other words to describe it.
Now going to 96Khz seems a complete waste of time as it makes no difference in my stuff. 44.1 to 48k is marginal also but the 16 to 24 bit seems worth it. I guess HDCD was 20 bit so 20 bit would be good enough also and a pitty 20 bit HDCD was not more adopted. Being in a position to render finished tracks in the DAW to 16 bit and 24 bit without any changes on the mix / master bus means I can do A-B tests with exactly the same material with no changes to the mastering.
I use HD800 cans BTW. I would not pay 2x the price for a 24 bit version of an album, it really is not worth it but if the cost is the same for 24bit 44.1 vs 16bit 44.1 then you might as well. Syngate priced their first 24 bit digital download the same as previous 16 bit releases so no big deal.
If you want to do your own test if you have some 24 bit tracks then grab the open source audacity, import a 24 bit wav and export as 16 bit. Check the prefs for setting the dithering quality. You can then A-B yourself with a favourite track.