Well, now.
You're making a generalization by looking at very specific element of Japanese pop culture, AKB48; i.e. Idols. Then again you're also using the same generalization for Korean pop culture, so I'm not really sure how to respond to the question entirely. If you want to just compare Korean Idols (SNSD) against Japanese Idols (AKB48), then yes they are very different. They actually have the same goals and endgame in mind, but they package it in rather different ways. Also, while AKB48 tends to be more cute than sexy, they do have their sexy side. Just as SNSD has their cute side despite usually being more sexy. And each culture has groups that do one more than the other. There are plenty of sexy groups within the Japanese music industry and plenty of cute ones in Korea.
If you take a broader scope of both industries, Jpop and Kpop, you'll actually see that neither SNSD nor AKB48 are good representatives for their respective cultures. I'm not saying they're bad, rather I'm saying that one group should never, and will never, represent an entire music industry. If I let SNSD represent Kpop for me, I probably wouldn't be very interested in it--which is why I sought out other Korean groups to hold my interest. If you don't understand the appeal of AKB48, I suggest you try looking for other Japanese artists. If you want something that's similar in style to SNSD or other Korean artists, there are plenty.
As for Korean groups in Japan, they are doing well. The Hallyu wave has always been popular in Japan. Years ago it was BoA and DBSK that made the impact on the Japanese music scene, this time it's just everyone and their mothers. Some acts do better than others, SNSD and KARA do pretty well in Japan. Just like anything, there are two sides to the Hallyu wave. A lot of people enjoy it, support it, buy the music and fan over the groups--how else would it get popular, right? But there is a more silent force in Japan that doesn't appreciate it and does want the Korean influx to stop. But it's called a wave for a reason, and waves dissipate over time.