Tires are the dominant factor in my experience. (In deep snow ground clearance is also a significant factor.) Many videos [1], [2] on youtube corrobrate this.
For the non-professional drivers on public roads, AWD is not a safety feature. It's arguably dangerous as it gives false confidence as you exceed the limits of your equipment.
It does provide a convenience at low speeds (e.g. parking lots and driveways) as it makes it more difficult to get stuck but even there tires and ground clearance are the dominant factors.
[1]: https://www.youtube.com/watch?v=EC1E2eDt1JY [2]: https://www.youtube.com/watch?v=iXjzYbpt9Ow