While the Amiga indeed had the Dual Playfield at a moment no home system had something similar (I remember reading a lot about "Dual Playfield" back at the time on Amiga literature/magazines and I had no idea of what the heck that was), I am always very surprised on how many C64 games actually do have Parallax scroll.
But then.. you have Shadow Dancer on the C64 with Parallax scroll... and on Amiga it does not. And I'd still prefer the Amiga version any day
I really don't think Parallax is the main issue here.