I have a 2008 JKU CRD 6 speed manual and it tows great! I haven't had any overheating issues and you choose the gear and sit in it so you're not having the problem with the torque converter not locking out. I reckon manual all the way
I have 4.11 gears with 34" tyres and it's a great combination. I tow a Jayco Freedom Outback which weighs in at around 1.7t loaded and the JK is probably sitting right on it's gvm loaded (front bar/rear bar/long range tank/winch/fridge/tools etc.) I sit on 95kmph at 2000rpm in 6th gear and it tows with ease. Most hills i don't even need to shift down a gear as it's right in the sweet spot for torque. On my last 2 trips i've sat at around 13.5L/100km which i can't complain about.
here's a pic:
https://www.instagram.com/p/BIXRIvOj...tour_australia
In saying that though, I probably wouldn't want to tow anything much heavier as i think you'd start to labour on hill starts etc.