There is also report Evaluating and Selecting a Learning Management System (http://www.elearningguild.com/research/archives/index.cfm?id=167&action=viewonly&utm_campaign=research-lms13&utm_medium=link&utm_source=lsmag), but you have to register to download it.
In Czech Republic, there are no defined criteria for LMS, but Ministry of Education published criteria for e-learning courses (how should e-learning curse look like and what should it contain to meet Ministry's criteria for accreditation).
You don't provide the reason for your question, which might help focus answers. In my view, at least in tertiary education, there is a trend away from only using a single multi-component LMS such as Blackboard Learn, Desire2Learn, Moodle etc, towards using a suite of products that may include a large LMS, but which also includes a range of other specific products. At our institution, for example, the products include:
Moodle;
EQUELLA;
Turnitin - Originality Checker, Grade Mark & Peer Review;
Adobe Connect;
Echo360 & PCap;and
Mahara.
Each is selected to add specific functionality to the online learning environment.
I may recommend our research site Knowledge Management Research at the Royal Institute of Technology (The KMR group). Here you find an overview of ongoing research and links to forums and projects concerning LMS and the question of building a teaching and learning environment of Knowledge Elements.
Learning Management Systems are available as open-source as well as commercial products. The features offered by LMSs depend upon the model that is being used in their design and development by their vendors. It is the user who selects LMS based upon his/her requirements.
One advantage with open-source LMSs is that you can customize them and you can add certain features/functions as the source code is available. I have surveyed some LMSs in my research paper and presented a comparison based upon their features/functions. The link is as follows:
As noted above, there are lots of commercial and open source LMSs... not sure if anyone regulates them, but you might check out work being conducted in this area by the US Advanced Distributed Learning Initiative... you can find them at www.adlnet.gov.
Nowadays the question should be how to give the student the opportunity to build his personal learning system. Offering different modules (open source) and the flexibility to decide between contents, evaluations, etc. (freestyle learning) is the best strategy.