To a degree some earlier Catholic states actually exercised more authority over the church than did any states, Catholic or Protestant, after Westphalia.
Sorry, you are incorrect. Cuius regio, eius religio, the state-church system, de jure, was pioneered in Zurich in 1525. It was endorsed by Luther when he backed the Schmalkald League. Its first broader application was at the Augsburg Diet of 1530, then asserted by Henry VIII in the 1530s, then in the Augsburg Interim of the 1550s. Calvin opposed it.
It is not true that Catholic rulers exercised greater control over the Church. At the very least, the church in their lands was still an international institution. They effectively limited the pope’s power but de facto rather than de jure, except in France. That is very different from the de jure seizure of power over the Church by Henry VIII or by the Zurich town council and many other German and Swiss town governments and territorial princes.
By rejecting papal authority, Protestant rulers rid themselves of that pesky pope who limited their power—sometimes not by much but he was always there, threatening absolute control, for Catholic kings. In Protestant countries, he was
just
plain
gone,
out
of
the picture, de jure.
It made a difference. There are no de jure state churches in Catholic countries, only in Protestant countries. There is something like a de jure state church in Catholic countries of the ancient regime.
But something like is no the same as the thing it resembles.
Therein lies the difference.