I am from a UK institution.
One of the things you need take into account is which Blackboard products the institution currently uses. The part that most people are familiar with is Blackboard Learn, the part that studens generally interact with for course content. However there are other products in the suite such as the community system generally used as an institutional portal, content collection which as well as course material may also provide storage and other services direct to staff and students. Outcomes is another suite product that gives managment data about student performance
It is relatively easy to run a comparison between one verion of Blackboard learn and a version of Moodle but if other areas are used (and they dont work independently) then the work involved in replacing these would also need to be taken into account. That is not to say it is a barrier but does need to be taken into account.
From my perspective Bb is better in terms of supporting traditional learning which is management/lecturer led in a strucured environment. Moodle definitely scores highly with people who appreciate a more freeform student led environment.
I dont think that cost should be a predominant factor here because as percentage of student fees commercial products dont cost all that much. The decision should be based on which platform better suits education at a particular institution.
"The more professional it will be the more possibility to select Moodle instead of Blackboard."
It does rather sound to me as if your mission is to persuade your institution to move from one product to the other, which any report may of course do, but I feel for integrity it is important to show that you are conducting an independent review, rather than simply presenting a sales pitch for a different product.