Time for new tires..P or LT?

I've looked up a lot of threads on this, but I haven't found a ton of good info, other than "one can run higher PSI's". I will be doing a little more towing of my camper trailer this year, and while I realize the P tires can handle the load, I was wondering if it would be worth stepping up to LT (C load) tires to help a little bit with sway stability of the truck?

So basically at this point, I'm wondering, do I get a quality P tire, like a Terra Grappler, or do I go to an LT tire and realize the benefits of stiffer side walls. I think a D or E load tire might be too harsh, but I don't mind giving up a little of the softness for better usability. Any thoughts and/or tire recommendations?

 

Mileage concerns - P metric.

More stability/weight/slight increase in tread life - LT C rated.

 

For what it's worth, I switched from LT's to P and am happy with the P. I don't tow much, but when I have I didn't notice any difference.

I feel like I have a better overall ride and also saved a little money.