It's very hard to say since a
lot of songs in the soundtrack contain elements that are common to both composers (but then again, Taro Kudo only has Axelay under his belt aside from this so we can't be certain of his composition style anyway); the melodies and rhythmic styles of most of the tracks sound very similar to Adachi, while the heavy basslines and driving melodies are very similar to the sort of thing you hear a lot from Kudo in Axelay.
This is a complete shot in the dark, but personally I kind of suspect that Masanori Adachi composed most (or all?) of the tracks while Taro Kudo did some sort of "arrangement" for the soundtrack after the fact; as in, perhaps Adachi composed the bulk of the soundtrack as some early version, and then Kudo reworked the soundtrack in his own style to improve it? This would explain the stylistic mash-ups, and it would also explain why the people involved with Konami at the time never seem to mention Kudo in regards to SCV4 (as per CHz's most recent post here).
... Actually, this theory is sort of supported by the
beta soundtrack that came out in the leaks a month or so ago; all the songs still sound pretty recognizable, and still sound very much Adachi-like, but they're missing most of their basslines, have slightly less coherent melodies, and lack pretty much everything that made the final soundtrack sound so similar to Axelay. The more I think about it, the more confident I am in my idea, though of course it would still be lovely to hear some confirmation from either of the composers themselves.
EDIT: Come to think of it, if my theory is right/close then it
could also mean that the tracks included in the aforementioned beta soundtrack consists of everything Adachi did, and that the "rest" of the soundtrack missing from the beta OST is what Kudo did. It would explain why the "remixes" (Beginning, Bloody Tears, Vampire Killer) aren't in the beta OST, since Kudo would have arranged tracks from scratch that had already been composed prior to all of this (as in, Adachi did nothing for those tracks). "The Submerged City" never got a bassline or a Kudo-feel to it in the final version, and the final version sounds almost identical to the beta version here, so that fits in with the theory too. Granted, now I'm just making assumption upon assumption, but it's certainly plausible.