Maybe it’s a joke but there is a lot of criticism of quad sticks on here from hunters who haven’t put in effort to really learn to shoot with them and learn a new style. Quad sticks have dramatically changed my shooting and really decreased my chance of a wounded animal while hunting. The amount of improvement over a tripod was huge for me.
I would very much agree with you about quads being a more stable platform once you are accustomed to them...with qualifiers.
Practicing at the range vs putting them in the field (effectively) takes more than a few minutes to get good at it. I would also say that shooting from a tripod isn't much different, but the time to come up to proficient level is quicker. I would expect to spend several hours doing dry fire practice with whatever kind of sticks you plan on using.
The deployment of the sticks are where the majority of the problems occur. At the range, no issues because I'm the one setting up the sticks. On a safari things are different as the PH or tracker will be assigned this responsibility.
We took our own sticks (BOG RLD's) on safari and when we were sighting in our rifles, asked who would be in charge of the sticks. Our tracker, Norman said he would take care of it. We then spent the next 15-20 minutes going over what we would prefer when the sticks go out, followed by practicing this and getting comfortable with each other.
Whether you are using quad, tripod, bipod or mono sticks; this time spent with whoever will be deploying them is critical.
My two problems with the quad sticks is getting them deployed quickly and use on uneven terrain. For some reason quad sticks seem to take longer or the transition from the tracker to shooter isn't smooth. The tripod doesn't seem to have as much of an issue. The uneven terrain argument has been beat to death so I'll just say that tripods are better for this.
My recommendation would be to use whatever you are comfortable with but PRACTICE, PRACTICE AND MORE PRACTICE! Second, dance with the one you came with. In other words take your own sticks or make sure you will be shooting from the same platform you have been doing your practice from. Shooting from a tripod at home then being asked to use quads on a hunt will not yield the best results.
EDIT - I recently sold my carbon fiber quad sticks in favor of the BOG Adrenaline tripod for big game hunting. I also use BOG Adrenaline bipod for turkey hunting or for use in a blind when sitting down.