1st Gen When to battle Green/Gary?

I've played gen 1 countless times, and I've always wondered if fighting you're rival on route 22 had any advantage depending on when you activate the battle.
I'm curious to know if anyone know if anyone has looked into this in depth?

Thanks for any help! 😊

In Red and Blue it's an optional battle you can get if you haven't gotten the first badge, yet. There's nothing more to it.

In Yellow that battle can determine which Eeveelution your rival ends up getting. If you win against him in both the lab fight and the Route 22 fight he'll evolve it into Jolteon. Winning in the lab and losing/skipping him on Route 22 he'll evolve it into Flareon and losing in the lab and losing/skipping him on Route 22 will lead him to evolve it into Vaporeon.