I'll have to go with manual overall for a 4x4. Much better control in most conditions, especially descents. If you fail on a steep hill, you can shift into reverse and safely descend back down under control. Fail on a hill in an auto and there's not much you can do but rely on the brakes and hope you don't slide out of control.
Yes, rock crawling is easier with an auto and it is better in sand and mud because you can shift without losing momentum. Also, an auto can shift while submerged if the breathers are plumbed high up. However, autos are really hard to keep cool when slogging it in most off-road conditions, and the heat is transferred into the engine cooling as well.
When an auto breaks off road, it's usually finished. Similarly, when the starter goes on an auto you're done without a replacement. Autos are more expensive and complicated to repair, and usually heavier than manuals as well. Also, just look at any truly professional off-road vehicle and they're mostly manuals from the factory. The only exception I can think of is the Gelandewagen and the H1, both originally military vehicles, so probably aimed at ease of use by multiple drivers with differing levels of driving skill.
David