One interesting crossover could be Percy using his water powers to help Supergirl when she's facing a fire - based villain. Maybe she's having trouble with a foe who can control intense heat and Percy steps in to douse the flames with his ability to manipulate water.
It's hard to say who would be the most powerful. Supergirl has super - strength, flight, heat vision, and other amazing abilities. But Percy Jackson has his own set of powers too. He can control water, has super - fast reflexes due to his demigod heritage, and he's a great swordsman. It really depends on the situation. If it's a fight in water, Percy might have the upper hand. But if it's in open air and involves a lot of physical strength, Supergirl could be more powerful.
One inspiring Supergirl story is her fight against powerful villains to protect Metropolis. She uses her super strength, flight, and heat vision to keep the city safe. For example, when a group of alien invaders threatened the city, Supergirl was the first to stand up and fight them off, showing great courage.