Dolly towing

Actually, the very BEST thing for towing a 4X4 is the Warn kit that used to be available to put manual locking hubs on the rear axle. I installed a set on an old Tuxedo Park CJ5 some years ago. They were great! Just hook up, unlock all four wheels, and go.
I heard they don't make that kit any more.
EVERY 4X4 Owners Manual I have ever seen (no, I haven't seen them ALL) states DO NOT tow 2 wheels down, not even in an emergency.

Manual front hubs and a manual transfer case is the best setup for towing on a dolly or flat if you want 4wd.

No difference whatsoever!
In a 4X4 vehicle, the transmission isn't turning, the transfer case is in Neutral, with the transmission in Park or in any gear (I used to put my Jeep in 6th gear; I put the truck in Park).
In some AWD vehicles (such as a manual transmission Subaru), the transmission is put in Neutral. Automatic transmission Subarus must be towed on a trailer; they can not be towed four down or on a dolly.
SOME rear wheel drive cars that are four down towable can be towed on a dolly. Regardless of what some people say, not all manual transmission rear wheel drive vehicles can be towed four down or on a dolly.
A two wheel drive Jeep is not towable four down or on a dolly unless the drive shaft is removed. Come to think of it, that is how to tow a 4X4 Jeep on a dolly: Remove the rear drive shaft!

Does it make a difference if it is a Manual transmission or Automatic?

There MAY be exceptions, but the general rule is that AWD and 4WD vehicles, IF rated towable, must be towed all four down.

My 4WD Jeep liberty is not dolly towable. All 4 wheels must be turning.
Your toad may be different.

Thanks BarnyS for putting in the right place :)

Moved to Dinghy Towing forum from Towing.

No all 4 down vehicles are not dolly towable

Jeep manual says my 4 WD car is not dolly towable - FWD is ok