In very general terms, the differences between PS and PSE will be:
- PSE uses more "big button" solutions, where in PS, one does things by hand, but with the benefit of more, easily accessed control.
- PS offers CMYK, where PSE does not.
- PS can create Layer Sets, where PSE can only edit them.
- Do not think that PSE has added Adjustment Layers, but check me out on that one.
Of course there are more features in PS, even CS4, but those are sort of the "highlights."
Now, with the combo of PSE/PrE 10, one has some good interfacing to do things like rapid SlideShows, which allow one to link (sort of like Adobe Dynamic Link between PrPro, AfterEffects, Encore, etc.) between aspects of the two programs.
Now, and with that said, I have Photoshop, and also Premiere Elements and Premiere Pro. I have never been tempted to pick up PSE, to compliment PrE, as I create my SlideShows in PrPro anyway, and have no need for that linking between PrE and PSE. Still, others would not give up that back-and-forth SlideShow production, even if you gave them a free copy of Photoshop. If they move to PrPro, that SlideShow production is one of the first things that they miss.
Now, I have not read of any issues having PS, and PSE installed on the same machine. I have PrE and PrPro on both of my main machines, with no issues. I have just never tried installing PSE along with my PS, so cannot speak from experience.
Hope that helps a bit, and good luck,