This is definitely a SUPER opinionated area. I have the Vortex Harness Strap that I use in combination with a Horn Hunter Bino Hide, a cover rather than a pouch. I also have Alps RMEF Ridge Stalker X, which is a proper pouch. Finally I have the Vortex bino tripod adapter, which doesn't sound like this category but I keep on a quick-change adapter on a Primos tripod that also has a gun rest. I will often just leave it on there while hiking, especially in thick timber when I want to spot-and-stalk, moving slowly, never actually putting the binos away, and be ready for a quick change to a gun rest.
My favorite HARNESS is the primos one because it has an elastic strap that takes any stress/binocular swing out of each step while you hike despite being very loose on you. You also don't add any "pouch" weight (the bino hide weighs almost nothing). The way it's rigged, the binos attach right to the strap rather than to hanger straps, so it's really smooth to use. The clip attachment points slide up and down the harness so they feel like they stay one unit as you use them. If I'm glassing a lot during hikes, this is my favorite combination.
Next up is my Alps pouch which I use when doing general hunting, especially for grouse or deer and ESPECIALLY while "scouting" pre-season. My pattern there is about being slow and quiet than about covering ground, stopping every time there's a change in the view. "Let your eyes do the walking" style. I like that the alps unit is cheap, but also has some details that set apart more expensive pouches, like having a quiet closure, and having separate straps just for the binoculars with a quick detach. I can take them off and hand them to my kids on family hikes, or if I see something to react to, just drop them and grab my rifle (and they won't fall).
But both of these are clumsy in thick timber especially if I'm doing spot-and-stalk in there. In there, you're glassing more or less constantly, using the binos to do what your eyes can't do and "see past" the near stuff. With a pouch you're taking it in and out constantly, and with just the harness it seems to get in the way of a slung rifle a little more. So keeping it constantly mounted on my tripod (which doubles as my walking stick in there) I always have it at-hand and in use.
Look how much I just vented. If there's a point to all this it's that you have to choose what fits your style of hunting and personal preferences. There are several dozen products out there. Try 'em out and see what fits you!