There are always some who say "the manufacturer's checklist is the only correct one". Ok, sounds good.
In the official Cessna 172 POH, there are 32 items to accomplish in the Before Take-off checks. Only three of these relate to the run-up check.
32 items. At $300/hr, most likely.
Problem is, many of these items are drills not checks, and the POH does not differentiate between them. For example, item 32 is "release brakes", because that's the final step prior to commencing the take-off roll. "Release brakes" is sound advice, but it doesn't belong in any printed in-cockpit checklist. It is good advice in an expanded checklist, or in a how-to-fly manual.
No-one knows how to fly a Cessna (Piper, Jabiru, whatever) better than the manufacturer. But it is usually up to the poor old flying school to distinguish between drills and checks. That's why we have so many variations out there in the real world.