I have been tutoring privately since 2013 and teaching mathematics and physics since 1996. I have tutored well in excess of 100 students since I started and have covered all manner of syllabi in both subjects. I have taught GCSE, IGCSE, A-level, Pre-U, International Baccalaureate as well as AP Calculus AB (the American syllabus).
In my experience, the most important factor which is overlooked is the tutor’s subject knowledge. A close second is the tutor’s enthusiasm and ability to motivate the student. If I am not totally familiar with a syllabus, all the information that I need is available online. But if I don’t understand the topics covered, it is not going to be much use even if I know the syllabus inside out. All maths and physics syllabi share a large amount of common material. You can be sure that 80% of the material is the same.