Michael Penney raises a number of important points. The central-only solution has some limitations, particularly forcing everyone to use the common denominator set up an increasing the complexity of the course structure. Fully-decentral solution brings the opposite problems, particularly the issues you mention. The model I described ain't perfect but gives most flexibility. Let me repeat that the central service is, well, central to its operation. The independent instances are only for units that really want them.
MyFiles -- that could be restricted be only on the central Moodle.
Messages -- they should be discouraged in the first place since the bog Moodle for no good reason
IMHO. Their usage is very low here fortunately as most students use email or sms.
Forum post, blogs -- those are course-specific or department-specific, so no issue here. I mean single or multiple instances make no difference really.
which instance to access in order to attend a certain course -- if instances are department/program based, then there is no ambiguity: students quickly learn that all computer science courses are not on the central moodle but in cs-moodle. Those who get to the CS area on the central Moodle should find a link to CS-Moodle with appropriate information.
SIS integration -- that will vary a lot but I don't read much on moodle.org forums about any deep integration with SI systems. I don't see replication as in issue, particularly if LDAP or some other central service is used for authentication.
Statistics -- yeah, statistics are not so clean, but teaching is the reason for having Moodles not statistics and in my mind not absolute statistics but differential statistics for each instance is what is important.
Server administration -- yes, it gets replicated in some ways, but since each instance is managed by different people everyone does less.
Layouts and design -- it is a matter of policy. I don't really think that this would be a problem. On the contrary, variations in design may help users distinguishing the services. Instructors are free to rearrange layouts of their courses anyway, so variation of layouts can't be an issue.
versions -- Moodle basic operation does not vary that much among versions, particularly on the student level, so I don't see that as a real issue.
Plugins -- being able to use additional or custom plugins is exactly an advantage of separate instances. This affects instructors not students if they happen to have courses on different instances but that should not be that common if extra instances are department or program based.
advantages of having separate moodles -- I'd say that additional flexibility is the main advantage. As I said earlier, on the campus where I operate a departmental-level moodle instance, there is the central moodle and a couple separate instances. Those run on separate, local servers, although that does not have to be so (cf. Michael Penney's post). A few examples of differences. On the central server, instructors have to request having a course area created each semester. In our instance, we automatically create areas for all courses we offer (department caters to 5 study programs at this time). That would not be reasonable for the central server, of course. In our case, the usage of Moodle within department is so high (the psychological aspect of owing an instance and having local individual support is part of it) that only a few course areas stay unused. In most departments, only individual instructors are using Moodle. Another thing we have is an intranet-like area for our students, which would be not practical if inappropriate on the central server. With true permanent enrollment in them, so students stay signed up during duration of their studies, we have several courses that cover specific aspects of study programs. Aside from keeping all related info in one location that gives us push mechanism for reaching majority of students interested. We also have a number of 3rd party modules installed which are not available on the central service. Our instance has also a few dozen small and not so small hacks, so it works just like the people in the department want it to work. Language pack is also adjusted to make our users more happy.
about students -- operating in this setup for quite a few years, I can say that I don't see any real issues that students have with switching Moodle instances except for those who are not regular students (we need to create a manual access for them). Only a couple of our instructors have to also use central instance due to teaching multi-disciplinary courses. I never heard any complaints about that from them.
Having said all that, I should clearly state that Moodles here are used primarily to support presence teaching. Things might be different for online-only programs, distance teaching, etc. There is no single recipe that works for all.