I think the final question: which produces better musicians?... is almost impossible to answer. Of course, ABRSM produces musicians who have the musical skills *which are valued in the culture which produced the ABRSM system*. Valuable skills, but not necessarily the only ones to have.
Also, some countries seem to want every child to be able to play at a basic level. Others want a handful of global-standard stars...neither would be happy with the other country's yardsticks for a good musical education system!
Japan has a hotchpotch of systems...there are few grade systems which embrace as many instruments as the British and British-derived systems, but the big instrument manufacters have whole companies devoted to music education (and some of those have branched out farther into kids' tutoring/sports/dance or adult/senior citizens culture/education/activities). Those do have exams, but relatively few people take them. With group classes, though, people aren't likely to join an advanced class if they can't keep up.
Yamaha USA grade exams...note that grades run from 9 at the bottom to 1 at the top. There are more exams available in Japan than in the USA, of course.
Kawai Music School, originally just teaching piano, starts with toddlers classes and runs the gamut from cembalo and shamisen to opera singing and jazz guitar...I don't think they offer grade exams, but they have regular student concerts, and will prepare people for conservatorium auditions...they are in other words, a corporate version of your neighborhood instrumental teacher.
For piano, everybody seems to work through a couple of series of studies, which are used as a benchbark. You have to have finished the Czerny studies to be accepted as a kindergarten teacher in many cases, for example. When you go to buy popular music, you will often find a little note on it saying ("difficulty equivalent to Czerny No. xxx").
For violin, the Suzuki books have become a sort of defacto standard at the pre-intermediate levels, but from intermediate onward, things are much more fluid.
There is more musical education at primary and intermediate schools than in many countries. Not only are all kids taught melodica, recorder, and what we call alto recorder (but I think it might be tenor in "real" English???), they are supposed to learn to read music, sing in tune and maintain parts (the teacher makes each child raise their hand when they think they've got their voice in tune with everybody else's, for example), and recognize certain classical pieces. The snag is that there are no exams, so you can pass through school without ever mastering one tenth of what is in the very impressive curriculum.
There is a bigger emphasis on performance here - if you are not serious about music, then you learn to play as well as you want to or your teacher pushes you. Otherwise, you are supposed to get onto the competition circuit and PROVE YOURSELF!!

So it's not how well you can play, it's how much better than everybody else you can play that matters!
Finally (at last, they all groan), one problem with grade exams...learning 3 short pieces for an exam seems to result in people passing through their entire musical education without ever playing a "major" piece. I could at one time play flute to G6 level or maybe a tad better (I think!!!), but I was very sure that concerti and so on were not for the likes of oi. I'd never played through an entire concerto or symphony, so I didn't really know what to listen for when I listened to them, either. So if grade exams are the main part of your musical education, joining a good orchestra should be a momentous experience!