I've done both. This year I picked up a guy walking a gravel road along the W Rosebud, turns out he was doing a weed survey. I also picked up a family this summer that was touring on bicycle. It was during fire season and they were riding from WA to the Continental Divide Trail, where they were going to ride S to NM or some such thing. They were Australian and were about to set out on a section of road that would be primarily freeway. I was de-mobbing from a site with equipment and tied their bikes to a skid steer on a trailer and loaded them up. They were very grateful to get past this bad section (St Regis to Missoula). The youngest was an 11 yr old daughter, setting out to ride something like 2,000 mi of mostly dirt trail! I've picked up many others, and passed up far more.
I've hitch hiked in the US, Mexico, Guatemala, Honduras as I recall. Never had an overly exciting experience. I've passed on rides and riders, though. These days I only pick up someone in obvious need or with an obvious reason (broken car, shuttle needed, etc). I would never have my wife or a daughter pick up a hitch hiker--their safety weighed against their exposure is too great to risk for another's need.
