I doubt there are many who have used both programs to be able to offer a comparative opinion.
All you really need for skinning from any graphics program is the ability to handle layers, i.e. not Microsoft Paint. Both Paint Shop Pro and Photoshop Elements can do this and so should have no problem working with AH skins. Its more important that you understand how to use all your program's features than which one you use.
Personally I use a ten year old copy of Paint Shop Pro, which does me fine. The later versions just add digital photography tools which I don't need, although it sounds like you probably do.