It all depends on what type of deer your hunting.....if it's for any deer....AM is just as good as PM IMHO. But it does vary thru the season.
Early Bow season Sept/Oct - Evenings. I think most deer are bedded in the AM, though does will generally eat in the mornings too. I generally don't see that many shooters in the morning. Does mostly. Even then, shooters will be really tough to get before dark, sometimes you get lucky, but you have to stay till last possible light. Big deer don't move very much, but if you find one, it's patternable and likely in a batchelor group and IF feeding during light, will be killable. (Exception: Abnormally cold, high pressure, frosty morning....I've killed/seen big bucks move late on mornings like this, they have thin coats at this time and generally will move late if it's cold sometimes, and sometimes chase does, etc, and act rutty) Doe/Fawn calls can be productive
Pre Rut (Bow season)- I've found early mornings to be successful, if your in the stand very early and not busting deer out in the dark, I've also shot good deer at dusk as well. Tossup. Again, Frosty cold high pressure mornings a favorite for mature deer.
Calling Rattling, very productive at first light. Buck may get up and see what noise they heard in the dark in their bed. Killed several big bucks doing this and many more encounters....that didn't pan out because the buck hung up, seeing no deer where he thought there should be.
Rut Chase phase- Stuff gets crazy, see deer any time. Bucks move mid day. Dink bucks everywhere any time. Dawn and dusk still good. Frosty cold high pressure mornings see a ton of deer. Food almost useless, except as doe attractant. Does sometimes go on lock down and will avoid times when early morning, late evening movement when bucks are more active so they don't have to deal with harassment.
Calling/rattling/chase calling very productive, but might push does, or small bucks away.
Rut - Mature bucks with does....hunt where does are. Morning/Evening both good, hope bucks don't leave too early, come in too late for shooting light. Does usually are first on the food, last to bed. If a set of does go by, sometimes after they go by to the food, I will try a small buck grunts in an effort to get a buck that may be still bedded til dark to get up see what's going on. This has worked for me before.
Shotgun (High Pressure) - Morning is when most hunt, and push deer around I'm usually done hunting by that time or year, or taking a break from it, but mornings definitely better than evenings, as there's way more shooting, and activity, and setups should be in thick cover, either close to bed, or exit/entrance routes where deer will move from pressure. For instance, I sat Saturday all day, for shits and grins in a hopelessly low deer populated area behind my house. I was on stand at 5am, a tiny doe came thru at first light, then a big doe, (Don't shoot does) then 10 or so minutes later comes the hunter that pushed them too me, headed to his stand I assume. He moved off thank god, didn't see me, or worse come and talk to me, and I sat all morning. I heard maybe at most 6 shots all morning. From noon til dark moved to a stand right next to a bedding thicket , not far off the road, but loaded with white oaks right outside the thicket.....hoping a deer may have gotten pushed there in the morning and might pop it's head out at last light to eat. That didn't happen, but I heard O, yes ZERO shots. So much more activity in the morning. Generally never had luck calling much, when woods are pressured.
Post Shotgun/Rut/January - I think it's very weather and moon dependent. Deer move very little to conserve energy and bucks are finding areas with close food to bed to heal up. They move barely at all. But if you find an area with food with a buck in it, likely you can pattern it. However it may only move at night. Does will hammer food this time of year, and theres usually a buck in with them. Very similar to early season...hunt close to bed areas where they are patterned on food. But weather dictates more. I see a good fair share of noctournal activity though this time of year.
If the weather has been super cold and nasty for a week or so, I like to hunt that first day it gets sunny, warmer and above 30 and a bit nice. Deer will move on that weather change, very likely in the morning.