The issue is steel and wheel alignment. Steel just does not brake as well as aluminum; that compounded with out-of-round issues puts the rod-brake machines at a disadvantage. If your wheels are really round and both machines have steel, then I would expect braking to be similar as you experienced.
Those Kool-Stops really help. I tried a set of NOS John Bull brake pads and they really were just too hard (even though they seemed OK)- kinda scary!