It gets the job done, but it's not remotely as rewarding as catching them yourself after a tough battle. And the branching evolution tree, in which every Digimon starts out as a round blob with eyeballs and ends up all spiky and anime-bad-guy-looking is way more complicated and confusing.
Perhaps most importantly, the battle systems are one of the biggest differences. Both are turn-based, but Pokemon gives each trainer a team of up to six poke-critters who then fight mostly one-on-one and sometimes two-on-two battles. Digimon Dawn/Dusk instead lets three of your creatures beat as many as five enemies unconscious at once.
Some of us here in the office actually preferred the feel of these battles and thought the extra fighters made things feel more tactical. Others preferred Pokemon because Digimon's the eight-element type system (water types do extra damage to fire, etc) is less sophisticated and there aren't things like effort values, special abilities or personality traits to consider. Either way, we'll give them credit for branching out. Also, veterans should know this is tougher than past Digimon games - there are high-level creatures in here that will send your super-awesome team back to the training room with its tail between its legs, guaranteed.
Just as in Pokemon, you can trade Digis or fight other trainers online, and the single-player story is throwaway. In Dawn, you play a member of the Light Fang clan. In Dusk, you're part of Night Crow (or Night Claw. The game and box don't agree with one another). Either way, after a big tournament, a mysterious intruder messes things up big time and your team blames the other side and sets out to set things right. The quest is the same in both versions, though they'll explore the various locations in a different order.