Ash Ketchum's Sinnoh Region opponent Paul is the single best rival he has encountered throughout his entire Pokémon journey. When fans think about Ash's rivals, Gary Oak -- who spanned Kanto and Johto Regions -- often comes to mind. While Ash's competition with Gary is epic in its own way, Paul serves as a far better rival overall.
The reason for this is that Paul functions as the entire antithesis to Ash and his fundamental beliefs -- especially given how, by this point, Ash had already been on his Pokémon journey for some time. Gary Oak is a good starter rival to motivate Ash onward, but Paul exists as someone he truly needed to beat.
Ash and Paul Advance With One Another
The point of any good rivalry is seeing how the trainers grow and change with every fight. Ash loves Pokémon, while Paul is fighting a one-man war with them. Paul's arc is simply reconciling that his initial beliefs were wrong.
Ash and Gary first battled leading up to the Johto Region. Despite Gary being Ash's rival throughout Kanto, they never once actually battled in that region. On the other hand, Paul's battles with Ash result in Ash growing as a trainer. Three of his Pokémon evolve fighting Paul -- Turtwig, Staravia and Chimchar. Ash and his Pokémon are pushed to be better by their duels with Paul.
At first, Paul is mostly indifferent to Ash, seeing him as entirely absurd and unimportant. Paul's biggest swing in characterization is when he loses a battle to Brandon, and he starts to question his methods and begins to see Ash in a new light. However, it's only through his many encounters with Ash that he begins to show more warmth toward his Pokémon.
Paul, Not Gary, Is Ash's Foil
When looking back at Ash's first rivalry, Gary is not really a foil in the way Paul is. Gary is just an arrogant brat who's better than Ash, which leaves him incredibly frustrated and angry every step of the way. It's only losing at the Indigo League competition that pushes Gary on his own path of self-discovery. His compelling Orange Islands arc leads to maturity when he re-emerges -- but it happens almost entirely off-screen. Gary leaves Ash as an overconfident jerk but re-emerges as a matured, more seasoned trainer.
Paul's journey from borderline sociopathic trainer to a kinder, more successful one is shown entirely on-screen, battle by battle, over the course of Ash's journey throughout Sinnoh. Paul starts as a cold trainer who views Pokémon as tools, a counterpoint to Ash who sees them as friends. That ideological difference hides the fact that Paul and Ash have several similarities. They both want to be Pokémon Masters but have very different perspectives on how to get there.
Both release Pokémon on a regular basis, though their reasoning is different. Ash releases Pokémon so they can go on their own journeys -- such as Pidgeot fighting a war against Fearow and Spearow, Butterfree reproducing with its lover, and Charizard pursuing its own training. Paul releases Pokémon regularly because they do not serve him well enough. That right there shows that, while their actions are similar, their intentions leave them on opposite sides of the fence.
By comparison, Gary and Ash have few similarities. Yes, they grew up together and share a common figure in their lives in Professor Oak. However, Gary essentially is just arrogant. When we see him with his Pokémon, he honestly treats them pretty well, made more apparent by the time Johto rolls around. He's never cruel or cold in the way that Paul is to his Pokémon. While Gary is a compelling rival, he's not Ash's polar opposite. That makes him slightly less effective.
The Other Rivals Don't Compare
Ash has other rivals in the Pokémon anime besides Gary and Paul. However, they aren't worth consideration in this discussion. While Gladion and Alain are compelling rivals in their own right, they aren't as memorable as Gary or Paul. Other rivals, like Barry or Trip, are more forgettable figures. There are, of course, stronger rivals out there. Tobias, for example, is far stronger than Paul. Ritchie actually beat Ash in his first Pokémon League Tournament. However, power is not a mark of true quality of character.
The only competition here is between Gary and Paul due to how memorable they are. They stand as figures who really tested Ash's morals and skills as a trainer in ways that stronger trainers before and after never could. But between Gary and Paul, Paul is the more compelling, chilling rival.