P tires vs LT tires - tire sales conflicting info

I changed from P to LT tires on my Tundra. They cost more and I didn't notice any difference in towing stability. I listened to many people on the forum say that towing stability will be better. Just did not see it. The Tundra was very stable with the P tires and is still very stable with the LT tires. If I ever wear out these Michelin MS2 tires I will end up going back to P rated tires as I just didn't see the difference.