On the Web (for example, here), you can witness some hot discussions on what graphic app to select - Photoshop, Photoshop Elements, or Paint Shop Pro. Very often people say that Photoshop is the industry standard, while the two other programs are not. Well, perhaps that's true and if you make your living in the printing industry or professional web design, Photoshop is "musthave". For home use though, you may find Photoshop much too expensive, and that its low-cost equivalents can easily cope with your tasks. Let's try to summarize the main differences from this point of view.
1. Interface. Some users say that Paint Shop Pro has user-friendlier interface than its competitors, the others hate anything but Photoshop. I think it's just the matter of habit and personal taste. All the 3 programs allow us to customize their layout to a certain extent. Paint Shop Pro's interface is the most flexible - you can change almost anything here (see example); you even can make PSP mimic Photoshop.
2. Color and Tone. Leaving alone "one-clicks" (automatic and semi-automatic correction tools), Photoshop and Paint Shop Pro offer almost identical sets of adjustment commands. In Photoshop Elements, you won't find "Color Balance" and some other useful commands. All the 3 apps support adjustment layers (non-destructive correction method).
3. Retouching. All the 3 programs offer great retouching tool sets. In Photoshop and Photoshop Elements, personally I love the Healing Brush and Patch, in Paint Shop Pro - the Scratch Remover. For extensive retouching though, I prefer Photoshop.
4. Layers. Again, all the considered programs support layers. Photoshop offers the richest functionality here. Paint Shop Pro's approach to layer handling is a bit different from that of Adobe's apps. However the most often used techniques are about the same.
5. Selections. In Photoshop Elements, you use the same selecting techniques as in Photoshop, while in Paint Shop Pro some commands work in a bit different (not worse though) way.
6. Masks. In Photoshop, a mask always belongs to a layer; in Paint Shop Pro, masks are separate raster layers. However, the work principles and achieved results are very similar. Photoshop Elements only supports adjustment layer masks, but the raster layer masking can be unlocked.
7. Transformations. All the 3 programs allow you to transform, rotate, and distort images. For selection or layer transformations, the Paint Shop Pro's Pick Tool plays almost the same role as "Transform" menu in Photoshop and Photoshop Elements.
8. Automating tasks. Photoshop and Paint Shop Pro allow us to record command sequences and save them for later use. IMHO, Photoshop macro commands - "actions" - are a bit more stable, while Paint Shop Pro "scripts" are more flexible - even painting and retouching operations (not recordable in Photoshop) can be saved and replayed. Photoshop Elements can play some pre-recorded actions (available in the "Effects" and "Filters" palettes), but it can't record user's command sequences.
9. Tutorials, plugins, etc. No doubt, Photoshop is the champion here - 9 of 10 third party resources on the Web are devoted to this product. Although some Photoshop plugins can work with Paint Shop Pro and some actions (very few) can be played with Photoshop Elements, Photoshop users win here. In the meantime, the essential work techniques in all the 3 applications are alike, and after learning your program's basics you may be able to translate a Photoshop tutorial to Photoshop Elements or Paint Shop Pro terms. BTW, for this purpose I composed a tiny Photoshop to Paint Shop Pro dictionary.
Conclusion. For a photographer or amateur-designer, Paint Shop Pro offers almost the same capacities as Photoshop does, while some Photoshop Elements' functions are striped down - no automation, missing adjustment commands, etc. My personal impression is that Photoshop feels the strongest, Paint Shop Pro - the fastest, Photoshop Elements - the simplest. Anyway, before making your choice, I'd recommend you testing tryout versions.
Free tryouts of Adobe Photoshop and Photoshop Elements can be downloaded here:
Corel Paint Shop Pro tryout is available here:
Also see "Wat's new in Paint Shop Pro XI"