just use the method they'd prefer ... use it as a chance to learn about the differences/benefits for yerself ...
i've seen it in use - its swings and roundabouts i think ...
i think the 62.5 method may suit designers more - for more control over font sizes, whereas the small/med/large is used more with accessibilty in mind - for government sites etc - but you don't get as much control over every detail ... ?