I used to live in switzerland and had a swiss platinum card there. the supplementary cards offered were about the same as you mention.
the big difference was that when i got a supplemental green card, the number (first four digits) was that of a platinum card, not a green personal card. i used it in situations where i didn't want anyone to "notice" the platinum card. This is many, many years ago when the plat card was still the top dog. i don't think the centurion was out yet.
i'm not sure what you mean when you ask about the difference in services but a standard personal (green) amex does not have the same benefits as a platinum. but the supplemental card for a platinum is not a personal card. it's basically a platinum card that's green.
i believe this is very different from north america. i don't think i can even get a green version here with my plat. only the gold. and as far as i understand, the gold supplementary card is not even the same as the gold rewards card that people get here.
hope i'm being clear, not too confusing.