Whether in oak timber or sagebrush badlands, a jumped buck runs off a ways, then stops and watches his backtrail. If you show up, plodding along exactly where he expects you, he leaves. So don't do that. It's that simple. The particular tactics depend more on cover and terrain than the deer.
Most hunters believe whitetails react differently than mule deer.
Younger whitetails do spook more easily than young mule deer, but older deer of both species act very much alike. A couple of years ago I sat on a ridge in eastern Colorado and watched outfitter Tom Tietz take Pat Durkin after a big whitetail buck in the yucca and grama grass hills near the Kansas border. The buck moved on them three times, each time stopping a few hundred yards away in another draw, the wind and a ridge behind him, and wide-open country in front. Each time, Tom tried another roundabout stalk, coming in crosswind until they finally caught the buck looking the wrong way. Now Pat could have taken a long running shot early in the stalk, probably either wounding the buck or running him totally out of the country.