I rebuilt the electrical transfer case and mechanical transfer case before and both are almost same policy but lever and electric for switch. They are pretty easy than manual transmission. They are not really expensive for part.
How many miles you have on your Jeep?
4x4 (4WD) and AWD are different types. AWD comes direct from transmission. AWD is much more fuel-efficient, requires less maintenance work, and has higher performance than vehicles with 4WD. Most AWD vehicles are around 25MPG and most 4WD vehicles are only 15 MPG.
My Subaru always full-time AWD for 9 years or 130k miles and no problem with AWD system and perfect for bad weather but no pull/push (I won't recommend for that.)
4WD has high torque that would be good for pulling heavy objects such as construction, farming, and driving through rocky terrain. 4WDs have high torque that can pull heavy trailers and use snow plows but high maintenance work for it will easily break down.