A big part of what has made the current wave of South Korean idol pop so successful in Japan is obviously the image. K-pop's often crass objectification of young women makes for a welcome break from J-pop's often crass objectification of barely pubescent girls. However, laughable though we may find it, there are some interesting differences in the music too.
One criticism of Korean groups such as Girls Generation is that their music is simply a formulaic rehash of current American pop trends, while Japanese pop equivalents retain their own national identity. Quality of music aside, I think this is basically an accurate statement.
There is, however, a big difference between Girls Generation and, say, Lady Gaga. Girls Generation are produced, marketed, and handled along very similar lines to their Japanese counterparts. Their music is promoted alongside Japanese artists in Tower Records (perhaps separated into its own K-pop area, but more as an annex to J-pop than something intrinsically alien), and their music is frequently and increasingly re-recorded in the Japanese language.