I grew up hunting in a family that made deer drives and for years running deer were all I had a chance to shoot. For a deer to run out of the woods and stop they had to have a death wish. I couldn't begin to guess how many I killed running. They most assuredly are easier than shooting birds though because leading them is so much easier with a rifle faster than a 30-30. Shot a number with shotgun and slugs, but as long as it's close like bird range and the shotgun is one you shoot birds with that is pretty easy too. When you have a deer running flat out, they don't bounce and are much easier as well.
As for scopes, I always keep them cranked down to 1 or 1.5x. I shoot like with a shotgun, both eyes open, and don't really notice a difference. The last running deer I killed were with a 30-30 and they were already wounded. Shot them in the head, one about fifty feet, one about fifty yards. That was the only two deer moving much in the last fifteen years or so.
