Here we can dump all the alternate versions of the soundtrack to our childhood that we may have found.
In some cases we may still prefer the MSX version, whether it's because of nostalgia, but also because it may simply just sound better on the MSX sound capabilities.
Even then, it can still be interesting how those songs that are practically branded in our brain sound on different hardware, and/or a different approach in arrangement.
As the topic starter, I really tried to contain myself and not give like a hundred suggestions.
I'll avoid mentioning for instance NES versions - apart from certain VRC6 versions which can be quite interesting. Even if the NES has an advantage on MSX PSG music for having independent white noise, those versions don't grant enough of a difference (at least to me, but feel free ofcourse).
Especially with Konami game soundtracks that MSX and NES share, which use the SCC on MSX, it's not really a debate which version is better. ;)
I'll kick off with just these five in alphabetical order (along with some sneaked-in bonuses):
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Barunba on Turbo GFX
https://www.youtube.com/watch?v=HZujS6aIT6I
This is a fun and well made shmup by Namco, which was surprisingly only released on MSX1 and Turbo GFX (I always assumed it was an arcade port, but it's not the case).
If you haven't played it yet and you like shooters, play it NAO. ;) No, seriously. Try it if you didn't know it yet.
Anyway, if you happen to know the MSX version of the soundtrack, this one is pretty cool to hear.
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Dragon Slayer 6 - The Legend of Heroes on Megadrive (Sega Genesis)
https://www.youtube.com/watch?v=lWrGWZ92U-Y
The PC-88 version is allright and the SNES version is subpar, but this one is worth to give a listen.
Even if some songs have entire parts missing (most notably "Dungeon" and "The Voice of God"), it can be interesting to hear this music on "16-Bit" Sega sound hardware.
Without getting too technical, the set-up of 16-bit Sega is quite similar to MSX OPLL+PSG, but with some important differences.
I think this Hirofumi Matsuoka was drafted to re-arrange Mieko Ishikawa's songs and wrote some additional music (such as cutscenes, a dedicated boss battle song and a new final battle theme).
Even if you wouldn't want to listen to the entire thing, at least check out the "Title Theme" (link with timestamp) which has a really cool re-interpretation of that recurring theme in the soundtrack.
There's also a PC Engine version which I don't care much for, but maybe some of you will.
Also, there's an IBM PC version for Adlib (OPL2) which sounds surprisingly listenable (even if still not very good).
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Fire Hawk on PC-88 (OPNA version)
https://www.youtube.com/watch?v=v_iU9G2lokU
This one may be 'controversial' in that most MSX fans will probably still prefer the MSX2 soundtrack version over this one.
Even then, the OPNA version can be interesting for comparison, especially because it uses some additional samples (most notably a little orchestra hit) which adds to the music in my opinion.
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Hydlide 3 on PC-98
https://www.youtube.com/watch?v=_RdzesdMols
Unfortunately, the Sega Megadrive/Genesis version of this soundtrack is abysmal for the most part, while these PC-98 renditions sound more like slightly upgraded versions of how we know it on MSX.
The Famicon version may be interesting as well. Also note that the description of this video has links to recordings of many other versions of the soundtrack.
(speaking of T&E Soft, here is the Super Laydock soundtrack on Sharp X1 as a bonus)
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Testament on PC-88
https://www.youtube.com/watch?v=wiLyTqJ-F00
There are many PC-88 versions of soundtracks that used PSG only on MSX(2) (a lot of them are present in the Telenet Music Box which I'm hereby sneaking into this entry anyway).
Of all of those, I selected this one for my opening message, because I love this soundtrack so much.
If you listen closely, you can notice that the PC-88 versions of these songs were written before the MSX2 versions. In the latter version, the compositions are somewhat more refined.
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Ofcourse I know of many, many more, but it's certainly more fun if I yield the floor to other people now to come up with nice suggestions. :)