The main difference is in the construction of the tire. While P-metric tires are designed to work at regular pressures, i.e., for use in mid-size trucks, LT-metric tires have a stiffer construction that enables them to work at smaller pressures.
Hence, LT-metric tires can also carry quite a bit more weight, meaning they are perfect for people who frequently tow their trucks or carry a lot of cargo in the bed/trunk. These tires will also work better for off-roading, thanks to the tough construction that can withstand punctures and cuts much more easily.
Nonetheless, there are a few disadvantages to LT-metric tires. For instance, due to the stiffer structure, these tires don't provide a smooth ride, which you can feel on most roads. Besides, they are heavier, which can negatively affect performance, efficiency, and, most importantly, performance.
So, for most mid-size and even full-size truck/SUV owners, P-metric (or Euro-metric) tires are the way to go. They already come in good load ratings for most things you'll do with your truck and provide much better stability on the highway, along with a smoother and quieter ride.
However, if you plan to tow or haul, or you use your truck for work purposes, I recommend going for a set of LT-metric tires. In the end, use what the manufacturer specified, and you should be fine!