I have personally played most games for both franchises, as well as watched the animes, and I even had a little digimon keychain. And although my personal preference tends to be Digimon, I will attempt to be unbiased, and most likely fail.
Pokemon -
While the franchise is bigger, it lacks a real storyline. You start with one Pokemon, you catch more, you fight at gyms, get a badge, and then throughout, you have antagonists you have to battle and beat.
However, although it's been the same ever since it came out, the introduction of new Pokemon has made it more interesting. It adds a suspense sort of effect, making you question how it will turn out. Despite the repetitiveness, it has a very large fanbase, and is extremely popular among people of many ages -- My mother even has a tattoo of Umbreon and Charizard on her back! And I'll admit, I play and watch Pokemon games more often, and I own a Pokemon blanket and Umbreon plushie, and well as the newest Pokedex book.
However, Digimon -
The fanbase is much smaller, and I'm sure there are much less Digimon than Pokemon (I am not sure!). Digimon has a much deeper storyline, more mature. Characters die, there is a looming darkness actually threatening to destroy the Digi-world, and there is the wonderful thing called character development! Now, you can argue that there was character development in Pokemon, but a very minimal amount. In the end, the plot of Digimon's anime was much better, in many ways.
So what about the games?
Dear god, some Digimon games were absolutely horrible, and the same goes for Pokemon. This is my personal opinion, but Pokemon Channel was a very cutesy game, but in the end, it got dull extremely quickly, and eventually became repetitive. Several Digimon games were repetitive as well. I will admit, I do have bias here. Although the Pokemon games do offer a lot of freedom and sidequest sort of things, I find that Digimon games seem more interactive, funner. You can choose to Digivolve them into a couple different kinds, and make several combnations. (The same may be said for Pokemon, although by my count, I believe there are five-to-ten Pokemon in all that actually have variety in evolution.)
I believe, in the end, Digimon is called a rip-off because of release date, small similarities, and fanbase.
~Clockwork