Have probably done 100k in the past five years towing 3 ton loads & double that mileage with landcruisers towing in general since I've owned one. Never never had a spot of bother with auto boxes ever.
Once locked up in gear they are generally just as economical as a manual, but that aside from reduced economy they are way better for towing in general imho.
Obviously not all 4x4's are created equal
Comparing a lazy 4.2L TD to a stressed 2.5L TD they behave very differently esp behind an auto gearbox. Have driven both frequently & the difference is night & day.