It seems like every time I disappear from this forum for a few months and then come back, there's a new thread on the age-old Digimon vs. Pokemon issue. So, here's my big thesis on the merits/demerits of both franchises:
The Games
I love the main-series Pokemon games. They are ridiculously well-designed and detailed for games ostensibly made for six year olds, and there are few experiences in gaming more gratifying than rounding up your favorite team of six and raising them to the point of conquering the Elite Four and the Champion. On top of that, it's the perfect game for collectors. At least it was up until about Gen III. It takes a special kind of crazy nowadays to catch/evolve/trade for all 649 pocket monsters, but I digress. Pokemon is an awesome game, and it's why I'm here.
I haven't played all that many Digimon games (Just some of the DS ones, really), but I've never been impressed. At best, the Digimon World DS/Dawn/Dusk games are mildly amusing RPGs that are uncomfortably similar to Pokemon in most aspects except for the ones that really counted. The "World" consisted of repetitive and uninteresting dungeons, as opposed to Pokemon's comparatively sprawling and fascinating regions. Also, the mechanics behind the games are just less meticulously crafted and balanced. The system of evolutions is convoluted and inconsistent, the type advantages are simplistic and uninteresting, and all the grinding and fetch-quest missions can't compare to the sense of adventure that's present in Pokemon. Actually, I think the only reason I had any fun at all with those games is...guess what...
The Anime
...yeah, I'm a big fan of the Digimon cartoons. I remember the initial airing of the dub of Digimon Adventure (or just Digimon, as we called it back then) when I was in first grade; it was the first anime I had ever seen and it left a big impression on me. It had everything a kid could ask for in a TV show: likable characters, a strange and fascinating setting, awesome fights, funny jokes, intimidating and charismatic villains, good vs. evil and all the betrayal/redemption that comes with it, and (for me at least) technological themes (I was a nerd then too). It was one of the first movies/shows that really got me invested in the outcome on a weekly basis. I cared about the lead kids, and I loved the way they played off their Digimon partners and their parents.
As for the Pokemon anime, even when I was a kid and watching it at the same time as Digimon it didn't really compare. It was entertaining, and I was always fascinated by the world of Pokemon, but the characters were too flat and uninteresting. Ash, Misty, and Brock had nothing on Tai, Matt, Sora, Joe, Izzy, Kari, TK, and hell not even Mimi. They were funny and Pokemon battles were cool, but to what end? There was nothing at stake; every week Team Rocket would blast off again, and we all knew that Ash was never going to be a Pokemon master because the goal was just too massive. With the Digimon kids, we (first graders) actually wondered if they would get home, or if they would beat the bad guy who totally outclassed them. Especially watching the shows again as a teenager/adult, it is clear that while Digimon has a story to tell with character arcs and drama and the like, Pokemon has never been anything more than a weekly diversion/advertisement.
The only time I the Pokemon anime ever made me care was when that first movie came out (wow was that movie a big deal), and I cared more about Mewtwo than about Ash. And even if we're going to talk movies, the first two Japanese Digimon movies by Mamoru Hosoda absolutely crush the Pokemon movies with their artful direction and superb character animation alone.
tl;dr
Pokemon has awesome games, Digimon has mediocre-to-bad games. Pokemon has an uninspired and manipulative cartoon, Digimon has a cartoon with real heart that made me care.
Except for Digimon: Xros Wars. I can't believe I ever defended that pile of turd. Don't watch it.