The only dirt road I have done is my driveway (which is about 1/4 mile long). Judging from hitting service station and parking lot ramps at an angle, the rear articulates better than it did with the springs.
I had a Hellwig Bigwig rear (and front) antisway bar on there, that cuts down a lot on the freeway sway and body roll, as well as the sideways rocking when hitting ramps. I had to remove it, because the links they supply do not sit in the same place as the factory links. I put the spindly stock one back on, but the sway has returned to about what it was before with the stock bar - maybe a little better.
Most airbag assist kits these days mount under the frame between frame and axle. This is closer to the center line of the vehicle than the steel springs, so to the extent that they are carrying any load you are reducing your roll resistance by that amount. On this kit the air bags are where the springs were, as close to the tires as they can get. For the same spring rate, they should have the same sway/roll resistance. According to Firestone specs on the bags, the spring rate is a bit less than the steel springs without overloads engaged, and less still than the spring+overload. However the air bags are considerably more progressive. From that information I expected a bit more body roll and sway with the air bag suspension, but it seems about the same with the same bar. I am going to fab some links to put the Hellwig bar back on when I get time.
Travelnutz - good on ya for knowing the difference - I emphasized it because many people get the two confused. With this system you are not just replacing the springs, but also the linkages, an important factor because axle position and pinion angle are better controlled than with leaf springs.
SoCal - I have not liked air bag assist kits for the reason you describe, and the one I mention above. Also they reduce suspension travel a significant amount in many installations. If you return the truck to the same ride height it had empty after loading a camper, the whole load of the camper is carried on the air bag assists and the weak part of the frame.