I did the same thing in '03 when I had a ....never mind that won't help the OP looking for more towing performance pulling a 25' TT. He doesn't need more load carrying capacity from a 3/4 ton truck for that size trailer.
OP your '09 5.3 1500 is down on towing power compared to the later model 1500 5.3 engines and especially the 6.2 engine.
Drive both if your looking at new trucks. Also the NHT option is GM max tow option. Gives the truck a bit more GVWR/RAWR and the lower gear ratio for towing duties. Actual final drive ratio depends on year models if your looking at used trucks.