What year are the trucks? 

I don't think I'd believe the guy who tells you that a 1/2 ton chevy has more towing capacity than a 3/4 ton ford. People have their preferances in trucks models, and I'd let him voice his opinion if you were comparing 3/4 ton to 3/4 ton. But I'd rule out his opinion as be biased toward a GM product when he makes that kind of remark.

When the trailer is hiteched to the Ford, does it sit level?  If the hitch is too high and more weight is placed on the rear axle of the trailer, that may cause the sway. VS the the GM truck being closer to the ground and keeping the trailer more level.

If the trailer has proven itself to tow well, then the new truck's hitch height is the only real variable. The Ford vs Chevy thing is bunk.

A three horse bumper pull is very critical on horse placements. With too much rearward loading (one horse, back stall) the trailer will usually not track well. When we had ours, (an 18' box) the single horse always went in the front stall. With two horses, we used the front and middle stalls. The only time the rear stall was used was with three horses. Using this loading, we never had any tracking issues when it was pulled with two different vehicles and using no stabilizer bars.

When we set up our hitch, we went three to four inches nose high at the hitch when loaded with one horse.

 BOL  Gard

 I tried pulling a four horse bumper pull with my jacked up blazer with big tires. Sway city!!!  The larger tires would allow it to flex the side walls which started every time a horse would move, and the whole jacked up suspension just aggrivated the problems.  I told the horses to hold still, but they never listened.  I increased the tire pressure which helped a little.   I went to a 3/4 ton pickup.

Turfa