There's some overlapping between the two systems. Not much really but there are some admin features that are quite similar (like manage courses, students, etc).
However, when you get to the teaching and learning, I don't think there's overlap at all.
The main difference I see is that .LRN (or any of the other LMS integrations) have features that operate at a higher level.
For instance in .LRN, you can create a course and then add forums, news, surveys, quizzes, etc. All to manage your course level tasks like getting your students to communicate, share, submit assignments, etc. But these are course based tools that help you manage your course.
However LAMS is mainly focus on learning activities and the orchestration of learning. So as such, you can have one of your course level task to do a LAMS lesson or tutorial.
In this LAMS lesson, the activities are following a pre-designed (and hopefully well thought out) learning process. Each of the forums, quizzes, surveys, etc are meant to be done in a particular sequence, helping the student's learning process.
So I think the context in which these tools/activities are used is very different from an LMS than in LAMS.
Now, when you put them together, you sort of gain the best of both ways. You get all your course management tools (LMS) as well as your lesson specific activities and sequencing (LAMS).
You could just use LAMS for your course management. But I think LAMS is a bit to plain vanilla and basic. Whereas the LMS give you more flexibility.
I think a bit more than half of the people that use LAMS use it integrated with another LMS. Not just because they already have an LMS, but rather because it makes more sense for them.
I hope this helps.
Posted by Ernie Ghiglione