They are different programs. I work as a lab tech for a professional photography studio, and we usually use PS for fixing and airbrushing photos, and adding certain effects. However with skill you can be incredibly creative with PS.

We use painter for giving a standard image effects that make it look like an oil painting. Or you can flat out paint something on a blank canvas. You can do all sorts of creative things with it with some practice. But you really want a tablet for painter.

For pure art purposes painter is more creative software. But since they are quite different programs, its tough to make a valid comparison. And the thing is, we usually use them in conjunction with one another. However, there are free apps out there that are similar to PS (Gimp for instance) - but there are no good free alternatives to painter. So you could potentially get away with just having Gimp and Painter.

My advice always is, if they offer a free trial (I know PS does, not sure about Painter) download it, mess around with it, and see if it suits you.

Hope this was helpful, and good luck!