Shawny, I do most of my deer hunting in the coastal region of South Carolina, where it is local tradition to hunt using packs of hound dogs to get the deer moving. We hunt large blocks of land, normally 40-50 acres or more at a time. To minimize risk we do not allow rifles or slugs to be used, only buckshot. We put hunters on all sides of the property, about 150-200 yards apart. Then we put 3 or more packs of dogs onto the property at different locations. Each pack of dogs has 1 or 2 hunters with them who are called "drivers". The drivers job is to lead the dogs into the thickets where the deer hide. When the dogs jump a deer out of his bed they will begin chasing it. Hopefully the deer will run close enough to one of the hunters to get off a good shot. But because the deer are quiet and fast, and because the cover is usually thick, most of them escape. If you enjoy hearing hounds or beagles running, this is a very fun way to hunt. However, if you only want to kill trophy bucks, this is not the way to do it. Generally the shots have to be taken so quickly that you worry about making the shot first, and then you can worry about how big the deer is. In our club though, we had a problem with some guys shooting any deer they saw. So we put in a rule where anyone who shoots a deer less than 75 pounds has to pay a $100 dollar fine to the club. This slows down the trigger happy guys, and gives the yearling deer a chance to grow one more year.
As to how effective a way of hunting this is, I will say that it is no more effective, and probably less effective than sitting in a tree stand. When I do sit in a stand I can most often kill a deer every day if I wanted to. However, I did not get my first deer this year dog hunting until Nov. 13. But some guys have already killed three or four. So it is a matter of luck as well as skill.
To answer your original question, the main benefit I find is that I very rarely have a boring day when dog hunting. Even if I don't see a deer I know that at any second one may come running past me, and I always get to listen to the dogs when they are trailing. What I really love most is the excitement of having a pack of dogs coming towards you baying their heads off, and knowing there is a deer in front of them. For a hunter and dog lover it doesn't get any better.