This reply will be similar to Jorge's but seeing as how he already put his expertise into the post I will give the post a little lemon twist. I did remixed versions of the songs a while back using just the triangle wave from the Am version and all of the imported version channels but no VRC6. Like so. Here is Aquarius.
Castlevania III - Aquarius RemixAside from those extra channels, the remaining ones all can be reproduced with regular NES hardware. So basically that is what I thought the game should sound like. When I first played Aku Den I was far more impressed with the music than it's American counterpart. The funny thing was I wasn't getting any bass samples and of of course no VRC6. It wasn't until 10 years later when I first heard the song with all hardware working in concert so to speak. I see now why the music was so different from our game and better. Still I thought that even without the extra channels the music still sounded good it just needed to have triangle bass put in it. Why this was not done I don't know. Listen to the music on Akuden without the extra channels and you will hear how the Japanese version is still superior in many ways despite lacking bass and should have been put in the American version with triangle bass added in the place of sawtooth.
Beginning - Japan's version benefits from a stronger sounding drum track as the Amtrack sounds wimpy. I liken the JP samples to those used on Ninja Gaiden.
Clockwork - The two of these are pretty much identical and as such both are epic tracks.
Mad Forest - Definitely like the JP version better it sounds darker, grittier and edgier, it's edgier.
Anxiety - This one I think the Am version benefits due to having the bass making it sound fuller. I might need to remix this one.
Rising - I love this track on AD bare bones no bass. It you add bass it's just as good and I love the echo in this track.
Stream - Both versions are about equal
Dead Beat - I don't like the Am version's beginning part. Too much wa wa wa in it. They were going for a Jaws feeling here similar to Walking on the Edge in CV 1. The goal here was to creep up on you. Yep that's Castlevania.
Nightmare - Japan version. Listen to it bare bones no bass and it has a creepy skeevish feel to it.
Aquarius - Drums Jp version. All other samples Am version. This song should have been used on the last level before the Keep.
Demon Seed - I will give it to the American version on this one.
Deja fuck it it's Vampire Killer - With or without the channels the JP version is better but it is not better than CV1's version IMO.
Riddle - The American version is shorter. Winner JP version again.
Pressure - This is a simple track and because its faster I will say viva America.
Overture - I like Japan's version better it has an echo. I am not a big fan of this for encountering Dracula though.
Also I listened to the Palcom version music and I think that it suffers the most due to being slower than the other two versions.