Mud terrain tires are not meant to be driven on daily in most cases. Unfortunately, they tend to be noisy, rough, heavy, hard to balance.
All-terrain tires give up traction, with smaller tread blocks, narrower voids and less-robust internal construction and tread compounds. The tread on all-terrain tires is also permeated with sipes for traction, making them a great choice for wet, snowy or icy conditions were mud-terrain tires actually do not do well. The tradeoff for off-road traction comes in a much smoother ride quality, better handling, tread life, noise level and traction in practically every other kind of conditions other than mud.
If you do heavy off-roading, you will not be satisfied with all-terrain tires. They are the best option, for all-around on and off pavement back and forth travels. All the usual trips you would expect out of a light truck or SUV. If you expect to spend a lot of time playing in the mud, mud tires are about the only thing for that!