You can try lightroom and see how it works for you. Each has its advantages.
LR is a professional photography tool designed for photographers, it has image management tools as well as editing tools. Elements is a light version of photoshop, and is pretty capable at simple editing tasks, it tends to have less control over edits and is easier to use.
Like any professional tool, Lightroom offers more user control over edits as well as more editing capability. It also means more skill is required, and to benefit, you need to learn how to use it, you will be frustrated and miss out on 90% of the advanced features when just plunging in and expecting to learn by trial and error.
If you do not have 10's of thousands of images to manage, elements might work well for you.
I haven't used elements since Lightroom 2 came out, so I do not have actual user experience to compare the current versions of the two.