The VC10 has a pronounced Dutch roll tendency at medium and high altitudes, whereas - IIRC - the B707 seems more likely to do it on the approach, no doubt often with an element of PIO involved (for the newbees, that's pilot-induced-oscillation).
Although yaw dampers always make small, quick inputs to the rudder to correct incipient Dutch roll (which presumably starts with yaw), the recovery technique pilots use for recovering a developed one involves aileron, NOT rudder. On the VC10 at about FL 200, the trainer used to switch off the yaw dampers, induce the Dutch roll (can't remember how) allow the roll to develop to about 40 deg each way, and then tell the trainee to recover using full aileron/spoiler against the direction of roll just before the attitude passed zero bank. That worked well.
The VC10 has 3 rudders, each with its own yaw damper. Turning any of them back on stopped the Dutch roll in a couple of seconds.
Yes, the early B707s had a parallel yaw damper on the single rudder, which had to be turned off for T/O and landing. It wasn't very good, and the rudder pedals moved to reflect its inputs. I remember passengering in G-AYSI, an early dash-320, from Gatwick to Nairobi and she Dutch-rolled gently all the way there. Later B707s have a series yaw damper (like the VC10 and BAC 1-11), which works well and doesn't move the rudder pedals.