For me it depends on the gun's purpose.
All my hunting guns have traditional stocks (wood and synthetic).
My match rifles have both stocks and chassis.
I shoot NRA HighPower competition and an (quickly and easily) adjustable stock is a huge asset when shooting standing, sitting and prone within minutes of each other. I need a different length of pull for each stage to get the best possible hold.
My match rifles currently have McMillan A5, McMillan A3, and American Rifle Company XYLO chassis.
I don't like chassis with AR style pistol grips on a bolt gun. I've owned them and put thousands of rounds down range with them, but in rapid fire stages I get back on the gun faster and more smoothly with a grip like those on the A3/A5/XYLO.
For hunting, I don't sit in a blind or in a stand....I sit for a while, then I usually like to still hunt. If I'm on public land that is new to me, I'm usually moving very quickly trying to get the lay of the land, and see where there is and is not game sign. A chassis rifle would be fine if I was just sitting watching a large field from a blind, but when you're moving constantly while hunting, you've got your hands on a cold aluminum heat sink. One winter I practiced outside with my Eliseo RTS Tube Gun a couple times in 20 deg weather....my left hand and face got so cold from being against the aluminum...it was horrible. This is what's keeping me from buying one of those little Sig Cross rifles.
Also, as a couple data points. Most F-class and Benchrest shooters use stocks...weird custom stocks, but stocks. PRS shooters are pretty well split between stocks and chassis. My point is....both can shoot well.
Choose what you like the look of, the feel of. Also, don't be afraid to buy a used stock or chassis just to try it....if you don't like it you can usually sell it for what you paid, less shipping.
Good luck,
Ross