As a general rule override triggers are “less safe” than direct pull. The best example of a direct pull trigger is the great old Mauser two stage trigger. You can bayonet, buttstroke someone, shattering the stock if necessary, and that Mauser two stage trigger will hold the cocking piece back, preventing an accidental discharge. It has so much sear engagement that it will not jar off.
The override trigger was developed because a large number of shooters do not comprehend how to function a two stage trigger. On a two stage trigger, you take up the light first stage, and then the trigger releases on the heavier second stage. This is too complicated for many, and I have heard people complain how their military trigger has “too much creep”, when in fact the final stage was nice and crisp. Well that first stage takeup is lowering a thick slab of sear so the final take up only has a tiny bit of sear to move.
Because so many people wanted a single stage trigger, manufacturers responded and developed the override trigger. The override trigger is like a trap door. Put weight on the door, kick out the prop, and the door will drop. In order to have a crisp trigger release, there can only be a tiny amount of sear engagement.
Having a tiny amount of sear engagement means that sear engagement and trigger pull weight are absolutely critical adjustments. If the sear engagement is insufficient, you can jar the mechanism, and mechanical tolerances being what they are, the sear can be overridden. Also, if the sear spring is not tensioned enough, the sear will drop out of the way when hit hard by the cocking piece.
Another blasted fault of override triggers is that most of them use sear blocking safeties. An override trigger out of adjustment, and the rifle will discharge when the safety is released. This is something that has happened with Remington triggers and caused lawsuits. If you notice, on new Remington’s you empty the magazine with the safety on. The older Remington’s the safety kept the bolt from flopping open, but when folks took the safety off to empty the rifle, a troubling number of them got shot when the trigger mechanism got over ridden. A senior citizen, HM distinguished shooter I know, told me of two accidental discharges with new M721 rifles. This would have been in the early 50’s. He either knew, or personally saw the discharges. In both incidents the shooter was proceeding to empty the rifle. Both rifles immediately discharged when the safety was taken off. One of those discharges put a hole in the floorboards of a car!
Overall, there are too many blasted things that can go wrong on an override trigger, and I hate them.
Unfortunately, all modern commerical bolt actions use them.
Stupid is as Stupid does.