I went from P-metric passenger size tires on my Ranger, to slightly larger LT truck tires, with a higher load rating. The truck rides firmer, handles weight better and generally handles driving better, even when empty. The truck has 3.73 gears and the small change in tire size didn't make much difference in power or operation. The change was well worth it, to me.
I am going to do the same thing with my Toyota Tacoma, which has passenger tires on it too. Except, because the Tacoma only has 3.58 gearing and a less powerful engine than the Ranger and even smaller passenger tires on it than the Ranger had, I will have to change the gearing in the Tacoma, likely to 4.56. I know I won't be happy at all with the larger tires and the puny 3.58 gears, since I'm not happy with it as it is.
I went from a smaller size and lower rated LT-E truck tire on my F350SRW, to a larger size, similarly rated LT-D tire, then to a larger size, higher rated LT-E truck tire, because of high loaded rear axle weight. On that truck, I had already changed the gearing from 3.55 to 4.56 before the final tire size change, because the truck was originally underpowered and undergeared, even with the stock tires. Switching tires to the first larger size with the original gearing made the problem worse. Changing the gears fixed the problem.
You're only talking about a 1" difference in tire height, according to the page you posted. Unless your truck is already taxed on power and gearing, the small change in tire size likely won't make a noticeable difference.
In my opinion, towing or hauling any significant weight with a truck or SUV should always be done with at least an LT-D or E truck tire. Passenger tires have no business on a truck, especially one that is actually used to haul/tow something heavy.
Manufacturers put passenger car tires on trucks, to make them ride like passenger cars.
Trucks are trucks. Let them do their job and ride like trucks.