I presently drive a truck with 290 HP and 410 ft. lbs. of torque. What should I expect to experience if I switch to a truck with 353 HP and 360 ft. lbs. of torque?
A gain of 63 HP and a loss of 5o ft. lbs. of torque will result in any gains or losses?

Subjectively... That is, the seat of your pant feeling will be...
The higher torque engine will feel stronger starting out from a stop. When you hit a hill, the speed will drop less at first. The higher horsepower engine will need to rev high, but will climb the hill faster. Work (hill climbing) rate is a pure function of horsepower.

If you're comparing gas versus diesel, remember the way the engine speed is controlled. A diesel engine is regulated by the injection pump. Your foot tells the pump to run the engine at "X" speed. Without moving your foot, the injection jump will increase the fuel rate to maintain "X" engine speed as the hill is climbed. The injection pump runs out of fuel increase at some point and the transmission down shifts. When a gas engine encounters a hill, your foot is throttling the engine air/fuel mix amount. To maintain "X" engine speed you have to inrease the fuel rate by pressing down, opening the throttle.
There is no magic between the engines, just fuel burn rates