I'm not an expert in CJK decomposition, but I can share some of my knowledge as a native Chinese.
Both decomposition are purely structural I would say. It is suitable for computer processing (input and recognition). We also use this way to look up a character in dictionary (99% of it actually, there are exceptions).
So in a broad sense they are compatible. But just as different Chinese dictionaries may put the same character under different radicals (部首 bùshǒu), there is no guarantee of consistency and mostly depends on the editor of the classification. Nevertheless these discrepancies should be treated as exceptions rather than norm.
Reference on structural decomposition: http://chinesenotes.com/chinese_fonts_structure.php
More on CJK characters
Chinese character decomposition as a study is much more than that. None of the above decomposition referred to 六書 liùshū, the six way of Chinese character formation. I highly recommend you look into it if you are interested in Chinese characters.
Japanese has its own fixed set of phonetic characters (仮名 kana) and Chinese characters (漢字 kanji). It uses the rules in 六書 liùshū (mostly 會意 huìyì) to generate many kanji that is only used in Japanese and only have Japanese articulation.
Korean characters (hangul) are actually shapes of consonants and vowels packed in a square so it is also a fixed set of phonetic characters.
p.s. maybe a bit off-topic, sorry :-P