The only time I see "Complete" used in the Japanese titles is a Saturn re-release of Silver Star which claims to add support for the MPEG Card add-on, so I assume it was probably more complete in relation to the standard Saturn version.
Otherwise is more complete in Victor Ireland's mind.
I actually remember the MPEG-Card version for the Sega Saturn, one of the best things about was, that you could put the disc into a PC and watch all the videos from the game (including the nice opening and Luna singing on the boat scene) with a normal video player, since they didn't a proprietary Saturn specific video codec, great thing in the pre-YouTube days
But I didn't remember this specific version was called Lunar Silver Star Story Complete which is kind of misleading since people might expect additional content in the game and not just a little better looking video sequences.
Coming back to this great 2.0 patch, I did a little research about the added song for the Star Dragon Tower and checked out, which music was being used there in the original Japanese game and having played the PS/Saturn version just once I made sure if it was used again or not.
Here you can hear the music used in the original Japanese Mega CD version, it is the same as in the Blue Spire:https://youtu.be/TSakbrq-b_E?t=5519
And here the Star Dragon Tower in a video someone playing the PS-version, here the music from Zophars Domain is being used like in the Japanese version but they didn't add their own song again:https://youtu.be/rBcSrqGvnWQ?t=144
Like I said, the added song by Working Designs doesn't sound very good (it kinda wants to sound dramatic but is a far to simple composition to make it happen) and it doesn't fit into the otherwise wonderful soundtrack of the game. And the fact that they didn't do this change again to the Playstation version tells you that probably most other players also felt so. So I'd be more than happy if by any chance a 2.1 of this patch could be made which undoes also this change by Working Designs, it might seem on the first sight that they added some value to the game but to me this was always the most annoying change they made to the game, more than the controversial paying magic exp to save change