First of all what is one and what is the other. Well Moodle is a class management system, think class websites. You can give grades in Moodle, and for the most part only the instructor can see student work. Structured and organized by topics or weeks, Moodle allows instructors to guide students through the learning process and evaluate their performance. When the class ends, the user data is customarily wiped out, and everyone gets a sense of closure. It's basically a conventional class minus the paper.
Now Elgg on the other hand, is a much more social, equal, democratic, student-centered (or person centered) system. Everyone has a voice, and your files, and presentations live beyond the classes they originate from. This is a place to evaluate your own performance, allow others to comment, and be part of a dynamic community. The creators of Elgg call it a "learning landscape", a free exchange of ideas tailored to the individual. (It's also great for file storage and backup.)
So which one is better? Anyone who tries to argue one or the other should prpbably take a step back and look at the big picture. Co-existence is the key here, we need structure, and (by "we" I mean the students) and Moodle provides that by breaking the class into topics or weeks, plugging in resources and assignments, and ultimately giving grades. Elgg is for the students to shine, publish their work, express themselves, and over time reflect on what they've learned. Used together, with each being tied to the different approaches tolearning they are designed for, our students get a sense of freedom and individulaism rooted in a structured foundation.