I just finished reading Dave Cormier's blog post PLE vs. LMS – disaggregate power, not people. and I have to agree that the difference between the two is who holds the power. As Dave says, an LMS gives the Institution the power, and PLE gives the individual the power. However, I believe that a LMS can be part of a PLE. If as a student at an institution, I am required to use an LMS, then it most certainly does become my PLE. I just have to make sure, that i can move my learning from the closed LMS to my LMS when i am no longer at the institution or when the course is completed.
I would also raise the point, that some learners may feel safer learning in a protected environment provided by a LMS, as oppose to using similar tools in an online, open environment. Not all learners are the same or have the same tech level (for lack of a better term) which would make their use of a LMS a better option for them.