I haven't used a recent version of elements, but I think it has started to incorporate a bit of the organization into it.
Basically Lightroom will do most everything a photographer needs short of heavy duty editing (HDR, pulling a face from one photo into another, etc). Elements can do most heavy editing (not as much as full Photoshop... but still a lot) but leave you hanging on the organization/cataloging/bulk processing.
We shoot over 100K photos per year and if I had to chose one or the other, I'd stick with Lightroom and limp my way through editing with Gimp (or other free programs). I'd estimate that less than 5% of the photos we shoot need anything in addition to LR.
But it all really boils down to what you need to do, and how you want to do it. I could see arguments going both ways, depending on the intended use.
Just realize that while LR can't do the heavy duty stuff, it certainly can do a LOT of typical editing for photos.
I'd suggest downloading both trial versions from Adobe, WATCHING SOME VIDEO TUTORIALS, and then play with them both for a month and decide what fits your needs the best. And to reiterate... don't try and learn them yourself (especially LR), get some training material to see what they are actually supposed to do and how they work. I hated LR when I first tried it because I expected a PS replacement... after watching video tutorials that stepped me through the entire program, I fell in love with it (it still has its limitations/drawbacks).