Based completely off of their "first" respective eras (since as of now there are so many spinoffs and modifications to the games and storylines). For Pokemon, I would count the Kanto and Johto regions, and for Yu-Gi-Oh!, all of the episodes and cards pertaining to when Yugi was actually the protagonist on the show.
Both captivated our childhoods with fictional monsters and strategic card games, and not to mention the portable (and non-portable) video games. Based on all of these factors with the storyline in mind, which franchise kicks the other to the curb?