Short answer: Buddhism was indigenized in Japan by the 1900s, with a history extending back centuries and so was only a "foreign" religion by a technicality, but not in any practical term. That said, Buddhism in Japanese society had a very very high place, oftentimes intertwined with government, politics, and daily ritual. Korean Buddhism, since 1392, by design, was removed from society, and was a political pawn (emphasis on the pawn part). When Korea was annexed into the Japanese Empire in 1910, Japanese Buddhism was rich, diverse, and influential. Korean Buddhism was poor, decrepit, and seen as a corrupt and ultimately traitorous organization. Buddhism became more or less discredited in Korean society, and was seen as a backwards and ultra-traditionalist perspective that bore little relation to the modern Capitalist economy, of which Christianity seemed to be a part. In Japan, where Christianity did not accompany the modernity of the Meiji Resoration, it was proved that a nation could be developed, modern, and capitalist without mass conversion to Christianity.

Long answer: There was a similar question asked a few months ago which you can read my answer to here