Lightroom's Develop module and Elements Camera Raw use the same non-destructive parametric Raw Conversion software - Adobe Camera Raw, or ACR.
But LR is a pro grade application and Elements (PsE) is a consumer grade application. So the version of ACR in Elements is de-featured compared to the Develop module in LR.
I'm not yet familiar with PsE 12, so I don't know how much of ACR's tools, features, and functions PsE 12 has.
Actually I recommend you have both LR and PsE 12, because LR cannot edit pixels, but PsE 12 can.
In other words, PsE 12 can do a lot of editing tasks LR can't do, or that LR can't do with enough precision.