err, first, I'd have to agree with the person who mentioned bias in this forum (after all, it's jdorama.com) because a similar questioned was raised last year in the soompi.com forums which is a kdrama forum and the jdrama flaming was pretty intense ^^;
so anyhoo, i think that for the most part, the difference is in pacing - which one you like is a matter of preference. jdramas (at least the one's i've watched - pride, SOS, GTO, forbidden love, to heart, wedding planners, hakoiri musume, hero) tend to move a lot faster. it's not uncommon for the main guy to meet the main girl (or one of the main guys/girls if there's several) and in the same episode, begin to like them. given 2 to 4 episodes, the two could also have slept together and now be seeing each othe regularly. This almost NEVER happens in a kdrama. the first encounter alone is broken down into several and often times, there's no definite attraction between the main characters for a couple episodes. then the 'dating' period where they're not even officially a couple usually lasts for several more eps. and another key thing is that korean culture is more conservative in that premarital sex is far more taboo than in japan (or at least drama wise that seems to be the case). only in recent kdramas have the main characters slept together - before All In, only VERY daring series had something happening like that or if something did, it was justified (i.e. girl was raped or was a prostitute and was unable to "control" it).
there are many more things but because of this, the predominant focus in kdramas is characterization. There is MUCH more build up of the relationship. Rather than just a couple events, there are many many many events that happen that to make the audience sympathize with the characters. One of the most common criticisms of jdramas is their lack of characterization. a lot of times they go too fast and though you can see that the main couple is/should be together, you don't empathize with them. a lot of the empathy is left to the viewer's imagination/romantic tastes. a lot of times, the viewer is just expected to accept the plot (girl meets guy, two fall in love, conflict with other interests, etc). kdrama directors are a lot more geared towards showing audiences why the 2 should be together. often times this involves some type of childhood scenes and many many scenes of them being together so by the time it's over, you don't need to imagine. a lot of times with jdramas, like SOS (which may be a bad example), you're just expected to see that Manato likes Yui (or whatever fukada kyoko was named) and you don't really see why. I mean, you can say 'yeah, he likes her cuz she's cute and there's this one scene... blah blah blah...' But for a kdrama, it's more like... 'jesus christ, the 2 ppl grew up together, survived a war together, somehow made it through a plague, etc...' - that tends to account for the length of the dramas.
And speaking of length, the most common length actually used to be 16 episodes. Dramas are divided into 3 types - twice a week/weekend, daily, and 'long period' dramas. The twice a week dramas are the ones that tend to be 14 to 24 (quite rare that it's this high - usually stops at 20) eps long. The daily ones run up into the hundreds. And the 'long period' dramas tend to be about some historical event and tend to be 50 eps or so long.
Suffice to say, the most popular ones are the 14-20 ep drama series. Another interesting thing to point out is that the kdrama Winter Sonata was extremely popular in Japan and actually had it's dvd release there before it was released in Korea (though not much before). Furthermore, kdramas are by far the most successful out of all asian dramas in terms of asian market and overseas sales (i guess these are just statistics but they reflect viewer popularity).
Finally, koreans have this thing for tragedies. The most 'remembered' dramas tend to be the ones in which like 14 eps are spend bringing 2 ppl together only to have one of them die in the last 4. i guess this is more of a cultural thing. This is also why there's the stereotype of someone always dying from cancer. The first extremely successful kdrama outside of korea was autumn fairy tale (endless love in taiwan) which had the main actress dying of leukemia. Another very popular drama was beautiful days which had a similar premise - and even now, Stairway to Heaven has the main character girl dying because of cancer. I think Glass Shoes had a similar premise.
It is because of these series that the stereotype exists. The majority of kdramas do NOT have death such as this and anyone who says so, has very likely not seen many kdramas. Most of the people here have seen enough Jdramas to know that not all series have the charm of GTO or the lack of characterization of SOS. And yet, those same people prolly haven't seen All In, Delicious Proposal, Winter Sonata, Summer Scent, Law Firm, A Good Person, Da Mo, etc. None of those series have anyone dying of cancer. Albeit in some, ppl do die by being shot or murdered even. But the vast majority of kdramas does not have such an occurrence.
A last thing to point out is that only autumn fairy tale and Stairway to Heaven had huge fanbases in Korea. The other series were relatively popular but not big hits - they were much bigger hits overseas than in Korea itself which means that the audience preferred the tragic dramas - again extenuating the stereotype ^_^
Take care y'all
~zola