As above, consistency...
I used to absolutely loathe training heavy in the morning. Just couldn't do it.
Wasn't until I forced myself to take it up due to work, timing and other commitments in the evenings, that after a while I noticed little difference between the two.
Sure, if I train on a sat. or sun. morning after a good sleep in, I feel a little more pumped and aware, but once you're in the zone, you're in the zone... nothing should effect your focus.
I'm a member of a 24hr gym so there's no hassle in getting my 5am start.
Might be a bit harder if your job is a physical one, but I see some tradies etc.. there in the morning and they seem to be just fine.
Like anything, it would just take time to adjust, but worth a shot if your evenings are too hectic.
Edit : As an upshot, generally speaking the mornings are quiet as so you have free reign on all the gear. No having to work around or in with anyone else.