We use the evening hours... A Lot!
First, it is vacation so we really don't feel the need to be out of the room at the crack of dawn. We've been to WDW enough that we know what we want to do and what we can skip, so we aren't in the parks all day. We pick a park in the morning that we don't need to spend more than 4 or 5 hours in, then come back to the room, do lunch, hit the pool, nap, whatever. Then we go to an early dinner, (5 or 6) and then to the EMH park by 7:00 or so and close it. It's a lot cooler in the evening and we can get more done, somewhat less crowded.
Second, we have a 16 year old daughter who brings a friend. My wife and I can't hang like we used to, so the girls can go to whatever park they want and we don't have to do the marathon with them if we choose not to.
For our style of Disney trekking, Park-hopper passes are a must though.
So, to answer the question, evening, but we're flexible enough to do a morning EMH if there's something we want to do.