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. (*^_^*)