Ok... Here are some of my reasons for each... I got a six speed because I'm a man.. Oh wait, none of that... I got a six speed because they are way more fun to drive. They are also better in sand in my opinion (sometimes the auto won't let you get the RPMs high enough).. Probably same for mud.. One big benefit for me, was that I go into the woods alone a lot.. Whether it's exploring, hunting, or whatever.. If my battery or starter dies, I can just bump start it.. Another big pro for me was the ability to downshift in an emergency, or even just for normal hill decent offroad..
Auto makes driving in the rocks easier and less stressful, if you were going to make a rock buggy, most pros would say to do an auto.. That is why I am sometimes torn.. I love big rocks, but also love my 6 speed.. I make it work and love it.. Other reasons for an auto are all mostly just because it's easy.. Drink coffee etc..
I like to completely control my jeep so I will "stick" with my 6 speed..
My $.02
My ride- 2001 power wheel, 11" plastic tires, upgraded battery, boat sides, custom bumpers, tow hooks, new paint.