I read The Father Brown Omnibus after the Sherlock Holmes collection around a year ago, so again, this will be quite short as my notes are not very helpful.
These mysteries show more of the principal players in and viewers of the mysteries than do Holmes’ stories. Chesterton portrayed the mysteries with a less scientific/logical point of view and with more humanity/sympathy/empathy. Because of this the stories include more moralizing and consideration of motives.
Sherlock Holmes is scientific/logical; in his stories he almost always explains all of the mystery in its entirety, and the mysteries themselves are puzzles, enigmas. The Father Brown mysteries are more of true mystery with religion, romance, philosophy, touches of the supernatural, and they have lingering mystery in the end.
Father Brown is annoying in his “helplessness” and “bewilderment” (i.e. it makes him seem falsely humble). I know that he is right regarding other people misinterpreting his simple words, but he has been enough around people to know the common interpretations (since some things are so common that they are assumed) and misinterpretations.
I enjoyed these mysteries but less than the Sherlock Holmes. Father Brown is not as interesting and original (and brilliant and awesome) as Sherlock Holmes, and the quality of writing did not equal that of the Holmes novels.