Mature bucks just might pattern hunters and move after the woods have cleared,
but I believe the bucks move on a natural pattern this time of day during the rut. For me nothing beats midday... period. Whether it be on heavily hunted public land or heavily managed(lightly hunted) private property in Iowa. 9 times out of 10 the bucks are by themselves cruising- which is the reason I love midday as IMO a cruising buck is the most susceptible to being killed because they aren't either chasing erratically or tending a doe and are much easier to manipulate. I've seen the oldest and biggest bucks moving this time of day through doe bedding.
The biggest thing I've noticed (on private land), and saw first hand more than once is the big bucks sitting and waiting, in the thick a little in the timber, for what I can only assume is doe walking back to their beds and checking them out. One example was in Ohio on private land. On this particular property I liked to walk in at gray light to make sure the fields have cleared. Walking in I jumped my number one target buck, which was a 5yo+. He was bedded along a very heavily used doe trail 50 yards inside the timber. Later that morning(11am) he came through my stand site between doe bedding and winded me. He had his nose to the ground and walked very deliberately parallel on the edge of doe bedding(which I was set up 20 yards down wind of, and he came 40 yards down wind
).
One can say that it's probably the hunting pressure that gets these bucks moving midday, but I am certain it is much more or a natural occurrence. When you are one of two people hunting 400+ acres in southern Iowa, and sitting all day and consistently having some of the best action of my hunting career midday it is pretty convincing to the nature at which bucks move (a little dramatic of an example, but I've enjoyed great action here in SE PA).
To answer this posts question, during the rut, if I had to choose morning or midday, I'd choose midday.