Tv show:
Is this really a question? Digimon's main claim to fame is the show, and it was really awesome for a kid's show. And it felt more like a "Kid's show from Japan" rather than, "A kid's anime." Not saying that anime is inherently bad, but being less into that genre made it more unique.
Games:
From what I've played, the games aren't anything special, but they are enjoyable and try to bring out the quirks that make the Digital World so fun in the show.
Like at one point, where you see a door across a chasm, and have to defy logic and try walking over the cliff to find that the prerendered background is really just a walkable texture. >.>
Movies:
Pokemon has some fun movies, then some really stupid ones. Digimon... HAS NINE MOVIES?!
Well, I haven't seen 'em, so I can't judge.
Monsters:
Ooooh, this is a tough one. Pokemon is pokemon. I'd say that overall, Digimon has a better-designed bunch of monsters and a lot of 'em, but Pokemon has the best if you can pick and choose. I still feel that Feraligator is one of the best monster versions of a real animal designs I have ever seen, however simple.
Characters:
Same as in the show category. Digimon has tons of fun characters. Pokemon decided that the cast needs to meet a new person every episode, so Ash's Facebook Friend's list makes him look like a desperate boy trying to look popular.
Overall Premise:
Digimon.
However, Pokemon is vastly superior at world-building, but that isn't a category. :/
Soundtrack:
Pokemon. It has some really good chiptune and tons of media and spin-offs to draw from, and the Americanization of Digimon is a bastardization of the already mediocre original.