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I don't know America itself worked with the Pokemon-Digimon duality and why one of them was successful while the other was not.
But, speaking from South America, the games from either side had little to no influence. The games of each took much longer to become popular because very few people I knew owned a Gameboy, or a PSX, and if they did, it was even more rare that they would own either Pokemon on the GB or Digimon on the PSX. This is a really odd concept when you consider that the games should've been the main media for the franchises while the animes should've been a side to it. But, truth be told, if you had asked almost anyone what they thought of the Pokemon games, people would be surprised that there were games in the first place.
So, in short, the games didn't tip the balance one way or the other. What did it in SA, instead, was that Pokemon came out much earlier. I believe the spanish dubbing for Digimon in Latin America came a whole lot later than Pokemon, so by the time it did come out, most people thought of it as a rip-off. Of course, there were still many who became more fans of Digimon than Pokemon (including me, for a short amount of time), but the delay in the release of the anime episodes and the mentality that Pokemon was the original one was ultimately Digimon's downfall.
In fact, I see a lot of people saying that Digimon died after Tamers. When Tamers was released here, not a single, individual fuck was given. The franchise was long void of any popularity in South America before that.