They’re not the same thing. I have both. Photoshop is more for manipulating content, while Lightroom is for adjusting lighting and organizing. If photography is your thing and you do minimal edits to the content of your pictures, (healing brush here and there, basic hdr, and panostitching is about it) LR is fantastic all-rounder system. If you do graphic design, or like to copy paste stuff within an image, or between images, photoshop by all means! LR will not cut it. I found Photoshop Elements Organizer rather clunky and slow, and instead use Lightroom Catalogue, editing in photoshop when needed.
Now, PSE can do pretty much anything that LR can, but it is a larger, clunkier, slower system. LR is a real joy to use.
I’d say that PSE is a more complete system, but is a pain to use. LR is a real joy to use, but once or twice a year I will pull something into photoshop to do a deeper edit.
I’d suggest getting lightroom and downloading gymp free of charge if you’re anything like me. 🙂
Just my 2 cents, Have fun!
-nasa