Which is better to teach English for non-speakers, make a native speaker do the job or someone experienced in the language but it's not his first ?

Always experience & education are the best successful qualifications for the good teacher, it is not about native speaker or first speaker, it is about the good strategies the instructor learn & apply throughout his/her work experience.

It depends. If a teacher is real good, like me, but not a native, still, they can be great