I've never brought a deer to a butcher, but have been told how its usually run like an assembly line, and many times you do not get meat that came from the deer you shot, but from someone else.
If this is the case, then YES, it would make a huge difference from doing it yourself. Some people take great measure in field dressing a deer as soon as possible to cool it down, and some do Not. Some people are very careful on keeping the exposed part of the deer clean, so do Not. Some deer are bang flops, some are not, and end up with a lot of adrenaline getting into the meat.
I believe the preparation you do before your meat even gets in the kitchen, will determine how well it tastes on your supper plate. So when you butcher your own deer, you know if you do things right, you should end up with some tasty venison. If what I heard about bringing it to a butcher is true, you may get a lesser quality meat due to someone elses lazy habits.