I would hopefully pick the better teacher. I would base my selection on a whole host of factors, i.e., experience, attitude, education just to name a few. I would pay little or no attention to the TEFL course they completed as my experience has been that no one particular TEFL type course is a guarantee of a good teacher.

What you seem to be saying is that an average graduate of a Trinity or CELTA is somehow or other automatically better than a graduate of some other course. Utter nonsense.

To close your mind and restrict your selection of a good teacher for your students and school to holders of particular type TEFL certificates is to deprive your students and your school of some of the very best.

How many students do you know who go around saying, "My teacher has a CELTA!" On the other hand, I know many who go around saying, "My teacher is great. My English is getting better."

Students could care less what certificate their teacher has. Only that he or she can teach. No certificate can guarantee that. Not a one. Not even ones certified by the British Council.