Ah yes, the age old question. The one that raged across the playground during my childhood: which was better? Well, back then we all decided Pokemon was better and that Digimon was just a rip-off capitalising on Pokemon's success, because it was aired on television afterwards, when the "pocket monster" craze was in full bloom, and things like Monster Rancher were popping up as well.
But I digress. Between the two, I think Pokemon has withstood the test of time much better. I didn't care for Tamers or Savers, and after being told (rather vehemently) that Xros Wars is even worse, I've been put right off it. That said, I think the Adventure seasons of Digimon are by far better than any of the Pokemon anime seasons - the humour is just better, and that goes a long way with me - and I quite enjoyed Frontier as well, although not quite as much as I did the original series of Pokemon. The card games were both equally nonsensical, and Digimon had the better action figures.
When it comes to games, Pokemon wins by sheer volume and diversity. I've played the original Digimon World, as well as the DS version and Dawn. They were good games, but compared to the thousands of hours I've spent on Pokemon games...well, they just can't compete.
So to conclude, both are excellent, but whilst Digimon was better than Pokemon as its peak, Pokemon has withstood the test of time far better than Digimon has, and will likely continue to do so.