If Ash uses his strong pokemon such as Charizard, Sceptile, Snorlax, Swellow; even Bulbasaur and Squirtle, he would beat Paul without too much difficulty if he fought to the best of his ability. I think that his problem with Paul is that Paul has championship pokemon, but Ash is stuck with weaklings. Paul's attitude makes it so that his pokemon won't go that extra step it takes to take his pokemon to the limits of their ability and beyond, so Ash always has a chance if he fights smart against Paul. However, fighting smart will only go so far if the pokemon you have aren't championship material. Charizard, Snorlax, Sceptile, and many of the other pokemon Ash has access to are championship material and have that strong bond with Ash that Paul's pokemon probably don't have with him. However, Turtwig and Staravia aren't championship material from what I've seen. Maybe that will change in the future, but as it is, Ash needs his A team pokemon to be able to defeat Paul. Without them, no matter how close to his pokemon he is and no matter how smart he is in battle, if Paul brings in his A game, Ash will always fall just a little short.