It really depends. If you're talking about the anime, then I personally feel Digimon definitely wins that department. I recently finished watching Seasons 1 - 3 of Digimon and comparing the two shows, Digimon as an anime is a lot better executed. You really get to see the growth and development of the characters in Digimon and the strength in bonds between human and Digimon alike. When you look at the Pokémon anime today, it's almost as if you were watching it from when it first aired. Ash is still on a journey of collecting eight badges from a region and he's still trying to become a Pokémon Champion, which has no definite meaning to the term. Plus, every generation Ash and Pikachu get reset so it's basically starting the same recycled story over and over again. Although, they must be doing something right, because I'm still watching it today.
With Digimon, you start at Point A and you make it to Point Z by the end, with a whole lot of stuff happening in between that actually runs coherent with each other. Not to mention, the story of the Digimon anime gets pretty deep at times and really digs into a character, their emotions, their future and goals in a realistic point of view in a way that Pokémon has never done.
However, if you were to compare the games, then Pokémon wins. Just by sheer statistics in sales and popularity, you can tell the Pokémon games fare a lot better than Digimon. I have never actually played any Digimon video games, but I've always found myself enjoying playing Pokémon. At the age of nineteen going on twenty, I still enjoy playing the Pokémon games. Albeit, that doesn't mean it comes with times when I get rather bored of them.
Now, comparing the mechanics of each franchise, I actually prefer Digimon's take. Pokémon has a very simple way of doing things, and while it makes things easier, I don't mind it getting complex at times. However, I will start off by saying I like the aspect of a human and a Digimon being partners rather than the human being the actual Digimon. I'll admit, I've always liked the idea of having a partner Digimon for myself. I mean, who wouldn't? Unlike Pokémon, they can actually talk, so you can really connect and bond with it like a true best friend.
Other than that though, I like the fact that there's the Real World and the Digital World. It gives dimensions to this universe and it also gives a really appealing story when either of both worlds can affect the other.
I also like that a Digimon can revert back to its Rookie form and not have to stay in its evolved forms. But besides that, I like that Digimon, and this may or may not come off as morbid, can die yet still be reborn by having their digital data reconfigured. Again, this is a sign of just how much deeper Digimon can go than Pokémon.
On top of that though, Digivices are just plain cool!
Again, it just really depends. If we're talking anime then Digimon wins, but if we're talking about the games, then Pokémon is it for me.