I kind of feel that people think kdrama is much better than Japanese drama. I never watched a kdrama before and I just don't want to. I grew up liking Japan and their drama. I watched many Japanese drama and I love the plot a lot. The acting is alright but the plot and the music are great. I think that people don't appreciate Japanese drama as much as they like kdrama. Japanese drama doesn't always have a romance story in it. Japanese dramas also teach life problems and touching stories. 

But if you've never even watched a kdrama and don't even want to give kdrama a chance, you are actually in no position to judge if jdrama is better or worse or underrated compared to kdrama. Kdramas don't always have a romance story either, kdramas have touching stories and teach life lessons too, even tho I'm more into jdrama but I can fully understand kdramas popularity, I've seen a few kdramas and I've actually enjoyed them, maybe you should watch a kdrama and then judge, just saying
Hello ken thank you for liking Japan and our culture.I agree with you as a Japanese that I love japanese drama more than korean because they are better they have better plot.in korean dramas they speak too fast and the plots are similar every time.
Personally, I love Jdramas and Kdramas for different reasons, and I won't make a blanket statement that A is better than B. But . . . I do agree with Ken's initial statement that people think that Kdramas are better--think being the operative word here--and that they're more popular. The problem is, for international viewers these days (especially people like me, who don't understand Japanese at all), Kdramas are much easier to access than Jdramas, what with the availability of (legal) streaming sites. In contrast, the selection of Jdramas in those sites are very limited (and even then, sometimes those dramas aren't the best that Japan can offer).

My point is, I think the root of the problem is that Jdramas aren't as readily available as Kdramas.
First of all, I agree with PrettyDramas here. It really isn't fair to compare them if you haven't seen a K drama at all. However, there's nothing wrong with a disintetest in K dramas and a prefrence for J dramas. If you don't want to watch K dramas, there's nothing wrong with that. You should watch what you like. (*^_^*)

As for your question, though, it really comes down to two things. In terms of popularity, Korean dramas do take the lead, that's pretty much a statistical fact. There are loads of reasons why that is, though, and most if them have nothing at all to do with them being better or worse than Japanese dramas. Just as kura2ninja stated, Korean dramas are much more accessible, for starters. This issue is mostly due to Japanese companies who do not widen thier market. Plus, they have some of the strictest copyright laws in the world. So, not only is it hard to find J dramas legally, it's also rather hard to find them illegally, too, as they are nortorious for finding and taking down thier copyrighted material. 

The other answer to this question is personal taste. It is related heavily to what's popular, that is true, but for many, the lush production value and super pretty stars that Korea has do seem more attractive. 

Personally, I watch them all. I started out with J dramas, but over time, I was lured towards K dramas, then Taiwanese dramas and Mainland Chinese dramas. I do tend to like Korean dramas better overall, but I tend to enjoy Japanese movies over others. Again though, that's just my personal preference. (*^_^*)

I actually started watching Korean dramas first because as some of you said they are more accessible than Japanese dramas but lately I've been liking J-Dramas more than K-Dramas, I just like the Japanese culture more and some of the actors and actresses are more likable to me, I think more people like K-Dramas more because they have a bigger budget and therefore higher quality but as for story wise I think Japan is better but that's just my opinion.
I think both kdrama and jdrama are good in their own ways, but indeed when it comes to popularity kdramas are more popular 
I agree with PrettyDramas. It's a bit unfair of you to judge kdramas when you haven't watched them. There's nothing wrong with not wanting to; you shouldn't watch what you don't want to. But when you haven't, how can you accurately make judgments as you have? I started off with kdramas and tend to watch kdramas more mostly because I've become very familiar with them and the actors, and also because of their accessibility like others have mentioned. I also think the production quality of kdramas tend to look higher end. That's not to say I don't love jdramas though. But I think they've both got different things going for them. I appreciate the plot and storylines of jdramas and how they don't tend to drag on storylines like kdramas often do. But by writing off all kdramas because you think they're all the same without ever having watched one is a bit uncalled for? There are a lot of gems to find in the kdrama world. 
kdramas are popular bcoz they maximize their market (from OST to products they show), not much in the case of japan, in my opinion
I stumbled upon this thread by accident.  I thought of giving a response to this topic.  The sad truth is yes, K-dramas are more popular and more well-known to international audiences then Japanese drama.

You want to know the sad truth: Many of K-drama fans won't branch out to other Asian dramas except Taiwanese dramas.  That include J-dramas.

K-dramas fandom are the toughest audiences when it comes to getting them to watch J-dramas or any Asian dramas that aren't Taiwanese or Korean dramas.

Don't tell me some of you didn't read these:

Why do people usually choose K-dramas over J-dramas?

The 5 Most Common Comments about Non-Korean Drama  

Why do you think people prefer watching K-Dramas over J-Dramas, C-Dramas, TW-Dramas?

Just today I even wrote on Quora why J-dramas aren't globally popular compared to their Korean counterpart and why K-drama fans branch out to Taiwanese dramas: My post on Quora-Why aren't Japanese drama as popular as Korean drama?

I hope my post can probably give you a good explanation why K-drama fans branch out to Taiwanese dramas and never to J-dramas.
Cuz anime is more globally known compared to jdrama
@PohSeng,

That doesn't mean they shouldn't excuse themselves from cashing on the K-drama fad.  I mean in Latin/South America, after K-drama became popular in that area, Taiwan cash in on the drama fad and guess what, it worked.  Taiwanese dramas become the 2nd most popular Asian dramas in that region.
I think it's just a matter of preference (and specially for me, also mood)
There are times when I don't watch kdrama at all but I watch a lot of jdrama and vice versa...
I watch kdramas when I want to see typical romance drama... but I watch jdrama when I want to watch something unique and touching stories...
Because, I think.. Back in 10~15 years ago, Japanese romance dramas are much better than Japanese romance dramas these days -not all, i know-, so I'm kind of not really into Jdrama when I want to watch romance dramas nowadays.. (special exception for NigeHaji!!!! (^^) )
As someone who has liked Japanese music, anime and culture for a long time, I am comfortable watching and understanding the plot of J-drama than K-drama. Korean drama has universal appeal due to its, I don't know, maybe "cutesy" plot and acting. J-drama is kinda lacking when it comes to this. That doesn't bother me though. I like J-drama the way they are :)
Personally I love K dramas more....In fact J Dramas is what I hate-.- Mainly because mostly all the J Dramas Iv'e seen were all tragedies,about 2 people who meet and fall in love and one of them have an illness and dies at the end .... Since I am a die hard romance fan,I didn't waste hours of my life,for a sad bloody ending-__- That's why I hate j dramas the most...I do like Hana Yori Dango,and all the power rangers,garo,and Kamen Riders but that's about it.....Kdramas are just pure perfection