I've always believed that Parodius Da! started out as a PC Engine project and perhaps like other Konami releases, got held back to support Nintendo's launch of the Super Famicom. The differences don't make sense otherwise. There was no reason to redraw some of the artwork to make it cruder or even just different and some of the missing parallax only makes sense if it didn't already exist in a previous version.
Stuff like these pics are the most damning evidence. Why design a background with tiles in repeating strips without scrolling like that, unless it was originally catering to the PC Engine? Why have a parallax layer scrolling verically but not horizontally over the layer behind it, unless it was designed with the PCE in mind.
Just the same, why release Gradius on a tiny 2 meg HuCard in '92 and cut some of the content and samples?