More than half the schools in Belgium are catholic, and virtually all (all?) schools are public.
Uniforms are worn only in a handful of schools, nationwide.

I've always attended catcholic public schools, but as I said, that's pretty normal here. Nobody pays any real attention to the 'catholic' part to choose a school for. Rather, the types of education and other factors like transportation are major factors.

Universities and colleges are also public. I attended a catholic college.
Being public is no detritement to our standing in international circles. Some of our universities have a solid reputation abroad.
Being public also has the added benefit that tuition fees are 500 euros for a year (excluding books and some basic equipment). My train pass was more expensive for a year. So when I graduated, I had no student loan to pay off.