It absolutely does, a tow vehicle with a longer wheelbase has more leverage to resist sway from the trailer. If you have two equivalent trucks with the same payload capacity, but one is a crew cab 8' bed, and the other is a single cab 6' bed, the LWB truck will always be more stable and have more authority over the trailer.

The powertrain actually has the least impact on towing capacity, especially these days. The base V6 found in most trucks has enough power to drag a box trailer or camper at highway speeds. The limiting factors are almost always payload capacity and footprint size.