Tax rates are often lower in wealthier areas, because 10% of a hugh amount, is still a huge amount, and 90% of a pittence is still a pittence. Zürich, although having lower tax rates has, almost certainly, a high tax take than SH. Therefore it has more money available for services.

It's like if I earn CHF200'000 and am taxed at 20%, and you earn CHF100'000 and are taxed at 30%, the tax take from you is still less than from me, even though your tax rate is higher than mine.

simples.