You seem to be (overly) focussed on significance testing. A statistically significant test between 2 means (ignoring for the moment that the choice of a nominal alpha level is arbitrary and subjective) may or may not mean anything even remotely interesting biologically. One of the larger messages from Anderson & Burnham was the reminder that the more defensible focus should be on estimnating and evaluating the 'effect size' -- the magnitude of difference, and whether or not said difference is bigger than some value that you (biologist) thinks is important. And that importance is determined by the biology of the organisms in question.
I totally agree and understand that. And it's not necessarily urgent for me to test for significance. I just want to tie together all the loose ends that keep hangin around in my head. I asked this question more in terms of understanding the connections/differences/suitabilities of both approaches.
For simple linear models, you can consider effect size by looking at the estimates of the beta parameters (given the appropriately designed design matrix). This is covered in some detail in Chapter 6. For RE models, you can't easily get there from here using the MOM approach. You can, however, do this in a fairly straightforward way using the MCMC capabilities in MARK (Appendix E), which are in fact more flexible than the MOM approach (albeit slwer, with slightly more complications concerning model selection). A demonstration of this applied to a similiar problem is in the first Addendum to Chapter 14. There are other examples scattered throughout the book.
Thanks for the tip. I will have to see if I can manage to get through it because time is running (MSc thesis). Will surely come back with questions...