hehe. Like everyone else here, my answer is "it's situational". And I'll add a 3rd category.
3. The guy who doesn't move. He's got a spot he knows holds fish, maybe a pod of risers, and works them for hours.
I'll try to generalize to throw some reasoning in, but it is a generalization, there are plenty of exceptions, and many of them for no better reason than thats what you feel like doing at that moment. I don't always choose the "best" way for that date and time. If I feel like workin, I'll work. If I feel like walkin, I'll walk. And if I feel like sitting on fish, I'll sit on fish.
Smaller streams favor the walker style. The stream ain't that big, and it doesn't take very long to cover the water in front of you. There's also more likely to be extremely shallow riffles and such which you know won't hold fish. On big water, it simply takes more casts to cover the holding water within range, and there's more holding water between the banks that a cast or two doesn't cover. Also, a "riffle" might still be 2 or 3 feet deep and is often the best water. A much greater % of stream has potential to hold fish.
Less fertile streams steer more towards the walker style. There's less fish per water, but they're more aggressive. You don't need to put it right in their face to get a strike, they'll go 5-10 feet. They'll also hit in the first few casts. If they haven't, they likely won't, and there's always a danger there's NO fish there. Best to move on. In more fertile waters, there's fish in every likely spot and you know it, and you gotta put it right in front of them, with perfect presentation, and even then it may take numerous casts before they hit. Working makes more sense.
Cold water steers more towards a worker style. Unactive fish don't always hit first cast, they take some working.
Crowds tend to steer towards #3. It's often a mistake from a logical perspective, you tell yourself that you should look hard for unmolested fish, and you're probably right. But in crowded waters, it may be a while before you find a decent spot with at least 100 yards or so to yourself again, and when you do, it's possible that spot has been worked over just like the one you're in, no way to know. Maybe you should move, but you're there, the fish are there, your having enough fun, got yourself into that trance, just go with it.