If I had a quarter for every time I've seen a Pokemon vs. Digimon thread online and a dime for every time I've seen someone say that Digimon is a ripoff of Pokemon...well, I'd probably be able to purchase a PS3.
The anime focus on different concepts. Pokemon is about a trainer travelling around the world and training to be a "Pokemon Master" and carries themes of friendship and perserverance. Digimon has always been, at the very end of it all, about saving the world from some dire threat, and in my opinion focuses even more on the friendship aspect of things.
Taking everything about their respective shows into account, I strongly prefer Digimon over Pokemon. I can only take so much of Ash and friends travelling around to compete (and lose) in various tournaments, character development happening only sparsely throughout a 150-episode region, and almost everything being the exact same as something before it, before it just gets...well, boring. Digimon, on the other hand, has provided something fresh and new with each series, and for that I am grateful; IMO, fifty-two episodes is just enough time to spend on a particular concept before introducing something new. Also, Digimon's season-long plots and character development win out over Pokemon's by a lot.
But then we have the games. I've never played the Digimon games, but from what I've read and heard, most Pokemon games are vastly superior. A lot of pokemon fans don't watch the anime; they just play the games, and for good reason. Yeah, we might've had the "beat gyms, stop evil Team(s), beat Elite Four" plot for four generations now, but that's not what draws many fans. Most of us play for the creatures, and some of us like to see how involving the Team's plot is this time around. And the gameplay...few things I've seen in my years as a gamer are more addicting than what the main series (and even a spinoff game or two) has to offer.
Now, the Digimon games' plots may be more in-depth than the Pokemon games'--I'm pretty sure they revolve around saving the world or something--but as far as gameplay and the overall fun factor go, it would seem that Pokemon wins.
So, in short...
Anime: Digimon > Pokemon
Games: Pokemon > Digimon