When saying LMS and PLE we imply that technology is involved. Learning management systems are platforms designed to deliver materials, collect assignments in a course, administer, track, and record the course/ program. Moodle is a good example of an LMS. This system is mainly implemented for formal courses and programs.
On the other hand, personal learning environments give the learner control over his/her learning process. However, they don’t necessarily imply self- education, but formal education as well. Web 2.0 technologies are mainly integrated into PLE, such as google, ibooks, and other tools that give access to information and materials on the web.
Both systems have their potential. Learning using LMS is organizes, systematic, centralized, time saving, easy tracking of work; whereas PLE is decentralized, tailor made, integrates both formal and informal education, promotes learner autonomy.
As to me integration of these two systems may yield truly significant results.
For a deeper idea of what these systems are watch this video by Stephen Downes.