I have been through several generations of PSP and currently have X5 which I occasionally use for photo work.
I don't have Photoshop, but from experience with PS Elements, I can say that PaintShop Pro is streets ahead in terms of user interface and user friendliness.
It has layers, and appears to do everything that Photoshop can do. I think that most people probably only use a fraction of Photoshops capabilities anyway.
Of course, it all depends what you want to use the program for.
For raw development, Lightroom is the way to go, and I wouldn't consider using PSP for raw development (AfterShot Pro is Corel's raw developer) nor would I consider PS Elements for such a task either.
TBH since I started using Lightroom I find very little need for any other programs anyway, since LR plus plug-ins does everything I need, and I rarely need an external editor.