Having towed with a few different gassers I can say that the diesel is hands down better, but you already knew that. For $15k you should be able to get a decent later model diesel.
Here's my experiences all with about 6-8K lbs behind (different objects/trailers but close weights), engines only, obviously 3/4tons were better than 1/2tons in suspension / handling.
Chevy 5.3L/4L60e/3.73s (1/2ton) - Decent, no slow down on hills (not much accelleration though). Keep an eye on the trans. Good mileage without anything behind it & unloaded, horrible during towing.
Chevy 6.0L/4L80e/4.10s (3/4ton) - Better power, but honestly pretty similar until you hit the hills, then you can move up them a bit better. Horrible mileage both unloaded and loaded.
Ford 5.4L (both F150, 3.73s and F250, 4.10s) - Dogs. Horrible hill performance, expect slow lane and loss of speed with 3.73s. 4.10s a little better, but still worse than the Chevy's.
Dodge 5.7L Hemi (1/2ton only experience, and this was with a 4k lb camper) - decent, pretty close to the 5.3L Chevy performance with worse mileage.
Dodge V10 1ton dually - (same 4k lb camper as the 5.7L) Towed very well with horrible mileage. Pretty good until the very steep hills then lots of shifting.
None of the above means you can't tow with a particular gassers (so F150 and like owners don't start a argument here), but given what I've driven and witnessed I'd stick with the Chevy or the Dodge gassers. Ford also offers a V10, but I have no experience. Again really with $15k you should be able to find a nice Dodge or Chevy diesel.