the solution is either a limited slip diff to transfer torque to the non spinning wheel or traction control to brake(create resistance), to send power to the non spinning wheel.
in situations like this, your regular 4WD will do the same thing without electronics or old school locking diffs.
Exactly, except that with a 4WD transfer case, both the front and rear axles are getting equal torque (that is, whichever axle is slipping will use nearly 0% of the torque from the engine, the axle with traction will be using nearly all of it)
Essentially a 4WD has the effect of a locked centre diff while an AWD may have an open or limited slip centre diff.
Also, many 4WD trucks/SUVs come with locking or LSD diffs. Our '98 4Runner has an electronically lockable rear diff, so assuming the front is an open diff, it will be a full 3WD system.
This summer my buddy and I took a couple factory Toyotas into a mountain off-roading trail. One was another '98 4Runner (5 speed SR5), and a '2002 Tundra TRD Off-road.
This was part of the route, a river bed that had been damaged by the spring floods, there were some deep ruts that left only a tire or two in contact with the ground!
We had to come up this river (literally)...
The happy beasts at the end of the road (there's a beauty waterfall to the left of the pic, we grabbed some lunch here before the drive back)
After making it back to civilization!
Anyway, the point is that for off-roading or serious winter driving (through deep snow) a 4WD system with LSDs on a truck or truck based SUV is the way to go. For everything else AWD may be fine, and in many cases 2WD is fine. Tires are the big difference!
edit: Wish I had pics of the hairy shit we were going through, but we were too busy navigating through it to get pics!