Depends a lot on your glassing style and if you want to use your binos on the tripod / how you use your spotter.
Backpack hunting for me is either elk, moose or sheep. Elk and moose I’m just using the spotter most of the time to verify legality and occasionally score with my spotter. I do my searching / spotting with my binoculars. That set up I carry a light and compact vortex ss tripod with their ballhead and outdoorsmans qr panner. For myself, having a separate pan function is a must. I tried without and it was frustrating trying to keep my binoculars (cl 10x30) on track, worse trying to control the spotter for tracking because of its weight (stx 65mm). Mostly here I’m looking at bedded and still animals so not really tracking.
Sheep hunting I swap out for the outdoorsmans fluid pan head. Much easier to fine tune quickly and the spotter plays a critical role. I beef up the tripod to the slik 634 too as the extra weight helps with the steadiness and I’m using heavier optics (el 10 x 42 and stx 95mm)
White tail, mule deer and antelope are day hunts from the truck. I’m using the heavier / bulky set up because weight doesn’t matter. The animals in that area are seldom bedded and always on the move, usually fast. The pan head is king here to control the heavy optics and I’m tracking them on the run.
For the range once I’m lined up I throw the digiscope set up on target once then adjust as I change targets. Either style would be fine here but I usually go panhead for ease.
So long story short - they both have their place. Ballheads shine for their compactness / weight savings but are best suited to photography or verifying with a spotter on non moving targets. In my opinion and experience anyway.
All that said - here is where my unpopular opinion comes in. I have a very generous hunting budget. I’ve tried a lot of different glass, heads tripod set ups etc.
Aside from keeping things clean and using the QR adapters to change heads between tripods and window mount I haven’t really found an advantage of the outdoorsman pan heads over something like a quality ball head (the vortex one I use is not lol) or the something like benro s2 head my brother runs.
Any of these options though have definitely performed better than the vanguard heads. I owned, tested and sold a few of the ph111v due to their play especially at distance. I tried out one of their 3 ways also (can’t remember model) but it was again sloppier and slower to use than others out there.