With great difficulty, Nancy. It is one of the most damning things about Learning Management Systems that there is, so little in the way of objective reviews of the LMS. I have used four such systems, WebCT, Blackboard, Moodle and Sakai, and of them all, Moodle, even with its flaws, outranks the others by a mile. WebCT was incorporated in BB, and I don't know if Sakai is still going, no interest there anyway.
The real issue is that companies who are producing a retail product for profit, do not want their product objectively analysed. Be bad for business I suspect, but the other side is that it usually can't be objectively analysed because for a study to be undertaken, it has to be used. That is, it has to have active Users, with active courses and so on, and test products are things not likely to be extensively used.
I doubt that many institutions would be willing to allow their systems to be seriously analysed. That's an old lawyer's trick, don't ask a question if you don't think you are going to like the answer. They may ask, for example, for a survey of User satisfaction but such surveys are usually as useful as reading the entrails of goats or some such, but usually such results are washed to present a more favourable outcome than it may deserve.
You could ask me, (or anybody here I think,) about Moodle, and I would try to give as detailed and objective answer as possible, but I am afraid it would be tainted with all the evangelical zeal of a born again Moodler.
Best option, Find out which schools, colleges and Universities are using which product and see if you can convince them to open up about their usage, their technology, their learning outcomes. Find out if such evidence actually matches the User Satisfaction survey.
Assess each product with a single set of criteria, if you can.
Then determine what questions are you actually trying to answer. Which, if any product tested, actually meets, or even comes close, the local, regional, national, required standards.
I'm sorry I am not being very helpful here, but AFAIK, Moodle is the only learning system that even mentions the word "Research", and that has to mean something positive, right?
What you might find useful are these two discussions in Comparisons and advocacy, both begun by Chris Kenniburg. 3 Ways to Stop Blended Learning in its tracks and Top Tech Tools to build a Learning Platform. They may not directly relate to the topics you are looking for, but both of them can inform you about some background that every learning system does actually face in the education space.
BTW, put your profile back up there, and keep in touch, these forums are likely to prove the best source of ideas about how Moodle is travelling.