When I have to compare two things A and B, can I say "a comparison between A and B" or "a comparison of A and B". Which is best ?
To keep things super-duper simple:
Both are fine. They mean exactly the same thing.
Use either one. No one will misunderstand you. Both are equally common in everyday usage. In fact, if anything, I would say that "a comparison of A and B" is perhaps more common, even though it may sound slightly less correct. This Ngram would seem to back me up.
If you compare A with B, then the comparison is between A and B. You could also say "comparison of A with B" as in the following sentence.
The immediacy of effect is assessed both with the observed data from phases 1 and 2, and a comparison of the observed data in phase 2 with the projected data from phase 1.
You could also say "comparison of A and B" as in the following sentence.
Counseling smoking parents of young children: comparison of pediatricians and family physidans.