This is a classic tank vs. tank war of attrition. While Ornn has better burst combos and late-game scaling via items, P gives you significantly better lane staying power. The lane is decided by whether you can bait out W before using your own CC.

A battle of sustain versus map pressure. Shen wins early short trades with Q, but your P allows you to stay in lane indefinitely if you farm well. Your main goal is to cancel R and outscale him in teamfights.

This is a battle of attrition against a high-scaling carry. You have the advantage in sustain thanks to P, but P means he deals hybrid damage that can cut through early armor. The lane is won by surviving his burst and timing your CC to catch him when he's forced to return to his body.