I've worn all the various kinds, and have Chicago Handcuff transport restraints as well as some Peerless chain cuffs and some hinged cuffs. For fun, I also have a set of Darby cuffs which can be nice. Hinged cuffs to indeed offer less mobility, though rigid cuffs offer the least. I find the chain more useful for very long term (overnight, car ride, etc) and hinged better for shorter term control (being kept immobile for some kind of teasing and whatnot). I've put some photos of my cuffs in action here so you can see them. Feel free to ask more questions and I'll do my best to answer

These are my transport restraints used creatively...but definitely not as intended!
Transport restraints in front. Note that I can't fully stand upright and the leg irons are short enough to only allow a difficult hobbling walk.
Multiple sets of cuffs on me, the strict being the black plastic-coated rigid cuffs. They had the effect of essentially giving my arms no twisting movement. I could only move my hands around a bit by bending at the wrist.