I would recommend Japan, personally. I've been to both SK (Seoul, Busan and Namhae) and Japan (Tokyo, Kyoto, Osaka, Hiroshima, Okinawa) and it's Japan that has me constantly wanting to return most.
I mean, Korea is awesome, but I got more of a feel that Japan offers a wider variety of experiences than SK did.
Of course, there's people who love K-Pop more than J-Pop, some love samurai flicks over the Vengeance trilogy, so your mileage may vary.
I love Korea a bunch, but Japan is just better for me. In Japan I spend ~$60 a day. In Korea, I would spend ~$45 a day and would include better meals too.
I have spent time in both countries. I loved both countries, but if I had to return to just one, it would be Japan. The people are straight forward and accommodating
For example, I found a quiznos buried in Tokyo (under a train track and hidden). The quiznos had a special: sandwich with bbq chips and med drink. If you wanted a different chip, no special. Not a big deal at all, but it's how Japan works. If you can adjust, then you will have a great time. Koreans, on the other hand, will not make a big deal. It's just a cultural difference. Both places are awesome, but I prefer Japan.
But, Korea is cheaper.