No, the audio is exactly the same except I think they added more voice samples (the music itself is the exact same chip track though). The CD version has an added cinema intro, that's it. In fact, the game itself is exactly the same, only worse. They changed the colors of some in-game graphics SLIGHTLY. Like the sky in the first level was changed from 5,5,5 on the palette to 5,5,6 or something ridiculous like that. Barely noticable unless you do a side-by-side comparison. Also, the CD version has to stop MID-LEVEL to load the second half of the level. That's the processing power of the System 1 card for you.
I'd highly recommend against buying a System 1 card for $25, or even for $5 if you have a flash cart. As you suggested-- just load the ROM onto the flash cart and do it that way if you must play the CD. IMO the cart is superior in every regard except for the lesser amount of voice samples.