Too many to address here. The short answer is that if you edit images one at a time and only need basic cataloguing capability, get Elements. It is very good image editor. On the other hand, if you need to be able to process, caption, keyword and catalogue large numbers of images simultaneously, get Lightroom. Lightroom handles 90% + of my processing needs, but lacks a few filters and layer features that Elements has that I find useful, so I use both. If I had to only own one, it would be Lightroom without question. Once you learn catalogue management it is a great program, and I really love that adjusted images don't have to be saved. Lightroom saves the adjustment recipe for each image, and these can be tweaked indefinitely without affecting the original image file or necessitating saving a copy of the adjusted image (this helps keep file management very clean and neat without multiple copies of images floating around). If you can only own one, best to download trial versions of both and try them before you buy. Most of the techniques you learn in one package will carry over fairly well to the other, so you won't be wasting much time if you decide against one on which you've invested time.
Both handle RAW images the same. LR4 is much better for me in cataloging my pictures, doing "quick fixes" on jpg, & printing. Elements 11 lets me do more advanced work such as layers and color/lighting variations. Elements 11 also has many filters in it & available as add-ons for special effects.
I look at them this way. LR4 is for enhancing and correcting photos (exposure, color balance, etc) and it has a powerful cataloging aspect. Elements is for more specific special effects...stuff like removing people from an image, changing backgrounds, etc. That's how i see the difference having both programs on my computer.
I use both, but prefer LR4 for the major part of my workflow. LR4 has a better organizer and more color/lighting controls and far better print controls. If you really want to be prepared for any creative situation, buy both and sign up for Lynda.com complete tutorials on both.