In my opinion, you can't talk about only the Organizer in PSE vs only the Library Module in Lightroom, because both are integrated with the rest of their respective programs.
Nevertheless, in my opinion, having used both, the Lightroom Library module is a superior piece of software compared to the PSE Organizer. By that I mean, Lightroom's Library module has more powerful tools, a smoother and more logical interface, and fewer and less serious bugs than the PSE Organizer (although I am not saying that the LR Library Module is bug-free).
Given the integration of the Organizer/Library Module to the rest of their respective programs, I would recommend that anyone who owns both programs use Lightroom's Library Module as the "organizer", and Lightroom's Develop Module as the primary editor, with PSE's Organizer as the secondary editor. It does not make sense to me to use thse two programs in any other configuration.
Of course, if you want to choose/buy only one piece of software, then that's a different story, and of course you would pick the one that meets your needs the best.
I've got both programs and have always used LR only until recently.
The problem is LR has major performance issues for me, and even just
using the brush to cover dust bunnies can take ten minutes to do half a
The constant waiting for photos to load in develop module, I just wonder
if Elements can do everything LR can do, there is no need for LR.
I suppose it's a case of start using it and see if I miss Lightroom. So
far in 2 days there's nothing I've found that Elements can't do that LR
can so I am interested in others' opinions.
I second Paige's advice. If you have strong needs for organizing and searching a large number of photos, LR is superior to PSE, both in functionality and the number of bugs. Adobe is still actively supporting LR, which is marketed to demanding professionals and prosumers, while it off-shored the PSE Organizer to a bargain-basement engineering team years ago. (I maintained the primary PSE Organizer FAQ before finally defecting to LR.)
So get LR for its Library and Develop module ($114 at Amazon) and the PSE Editor ($70) for the small percentage of time you need Photoshop's pixel-editing.