Timeline:
1975: Satoshi Tajiri makes a comic book called Capsule Monsters, comic book flops. Too soon?
1989: Tajiri founds Game Freak, creates Pulseman for the Sega Genesis.
1991: Capsule Monsters is reinvented as a video game starring a self-insert becoming the best in the world at something the world is obsessed with, which in turn is something that he made up.
1996: Pocket Monsters (Poketo Monsutaa) is released in Japan.
Tamagotchi is released in Japan and the US, becomes the fad of 1996.
1997: Digimon is released in Japan and the US as Tamagotchi for boys.
Pokemon cartoon begins
Digimon cartoon enters production; both cartoons are slated for US release in 1999.
Dec 16, 1997: 685 Japanese children are hospitalized after watching the episode "Dennō Senshi Porygon."
1998: Deciding that no publicity is bad publicity, Pocket Monsters is rapidly localized as Pokemon to avoid with Mattel media line Monster in my Pocket. 4Kids localizes the cartoon and quickly becomes a household nickname for Satan.
1999: Digimon is broadcast in the US on Fox, painfully advertised with "Brand new adventures, brand new characters, brand new show."
Digimon video game is released for PSX, sucks.
2003: After three seasons on the air, Digimon is canceled by Fox as the network dumps its entire Saturday morning lineup for "THE FOX BOX," a solid four-hour block of 4Kids cartoons.
Fox Saturday morning jumps from slow decline into total freefall.
(This is also about when Fox started screwing all of its shows like carpentry porn.)
2005(?): Toon Disney picks up all of the Saban shows that Fox threw out, including Digimon (and Power Rangers!), starts the Jetix lineup.
2009: Pokemon cartoon wraps up its eleventh season and the main character, who should legally be allowed to drink by now, is still a ten-year-old boy voiced by a forty-year-old woman.
Team Rocket still has not caught Pikachu.
Summary: Pokemon is a great game with boring cartoon and Digimon is a boring game with a great cartoon.
tl;dr: Pokemon and Digimon are both original IPs and have little in common, and they're both good.
Note: Outside of the Adventure series (Seasons 1 and 2 in the US) Digimon has no real continuity. As a franchise it's more of a "mythology," retelling similar stories in different ways. Season 3 (Digimon Tamers) was head-written by Chiaki J. Konaka of Serial Experiments Lain, hence the radical shift toward a darker universe.
Personal info: I was 13 when Pocket Monsters gave all those kids seizures, and at the age of 15, finding that my love for cartoons had not diminished, I was still fully ready to hate Digimon, but it took me by surprise and turned out to be really good. Unlike virtually any other kids show, it was able to show rather than tell it message. And yes, I a 25-year-old man, did just create an account on the Escapist to write a 500-word post on frickin' Digimon.