B757 has no spd prot in Vs i.e. the autopilot will fly to the stick shaker or to Vmo.
However, the 737 has loads of protection in VS mode, as long as the autothrottle and autopilot are engaged.
In Vs, if you try and climb too fast, e.g. 4000fpm at high alt, the autothrottles will advance to attempt to achieve the demanded r.o.c.
Speed will be traded off for height up to a certain point, and when speed decays to approaching minimum clean spd, then the VS mode will change to LVL CHG which opens the speed window on the MCP panel.
The 737 will then maintain whatever ROC it can given max N1 thrust and the limit speed of min clean.
The last resort is for the auto pilot to take over and pitch the nose down to maintain a margin above the stall.
The 737 has excellent speed/stall protection.
However, if the Aircraft has gone into Alt hold mode, it WILL fly to the stall if the throttles are closed, as the autopilot will prioritise holding an altitude against speed. This would only be possible if the autothrottles were also disengaged, which would be unusual under most circumstances.