PsychoLogical
Black and White, Yin and Yang, Light and Dark.
In the end, Paul’s Gliscor was never seen again after Grotle became a thing and Honchkrow stopped being used basically.In fact, one could argue Paul's Torterra was more of a mentor to Ash's then a rival and if there was one of Paul's pokemon that Ash's Torterra had beef with.. it would be Honchkrow.
Pikachu -> Electivire
Infernape -> Electivire
Torterra -> Honchkrow: never resolved.
Gliscor -> Gliscor: not really a rivalry, but after it's loss in it's evolution episode, it kinda had something to prove toward its former packleader, but this didn't get resolved.