Capt. Rex Havoc,
There is no appreciable difference between the high level handling of a B737 and a B747 Classic or -400. If anything, the various B737 models are marginally less stable.
The high level handling of the B747 was a big improvement over the B707, the -400 a big improvement over the Classic. The B707-120, and the even shorter QF -138, with Yaw Damper off, really took concentration, but the B707-300/320 with the Yaw Damper off were not so keen to dutch roll. With Yaw damper on, just concentrate ever so slightly less.
The B757/767 at high levels are interesting, because of the relatively low wing loadings, you have to work at it.
I have, over the years, regularly practiced hand flying at high levels, up to FL410, and any pilot who is not competent to hand fly an aeroplane throughout its flight envelope is not, in my opinion, fit to be on the flight deck.
Hand flying at high level, just straight and level does wonders for your scan, makes sims a pushover.
Today, we have the luxury of multiple autopilots, but it was not always so, how do you think we got on if the A/P was U/S ----- hand-fly all the way. Three of us did it SIN-JKT-PER-SYD one night, slept well when I got home.
Tootle pip!!