Tom,
I guess it's personal preference. Hard to find buddies that want to dive in the middle of the night -- then again, this is one of the main reasons many people solo dive...And of course when you have a 4 and 6 year old who are going to come bounding into your bed at 6:30AM the next morning.....diving at midnight with a 1 hour drive home can become a little old. That being said, I may try some early morning diving this spring to see what it's like to dive just before dawn. I think the dive shops schedule them earlier in the evening out of convenience -- also, they may not get many people to show up if they frequently schedule them in the middle of the night....
There is something to be said for trying your first night experience at dusk -- especially at new sites or if you are still mastering equipment set-up. Having a little daylight to help get yourself oriented to the site and getting your gear put together can be helpful.
I've done all of my night dives just after dark and I find them all interesting -- lots of things to see that are hidden during the day and the added "excitement" of the dark. I'm still marveling at the 10-12 pound lobster I saw on a night dive last summer...HUGE. Perhaps my favorite are the schools of squid we often see here in New England. On many occasions I've had several of these guys (up to 12 inches long) hovering inches in front of me staring right back at me -- transluscent color -- very cool. I also love snorkeling back in at the end of shore dives with my lights off, occasionally waving my arms in front of me and watching the luminescent creatures light up the water.
Enjoy!