You might be right. I’m not aware of those stats. Generally the catholic church has the same problem of declining membership that the mainline protestant churches have. My church has plenty of refugees from mainline protestant churches as well—including me.
I can't, and wouldn't want to, compare the two in any way, except to note that they both have strong male leadership and participation, place greater expectations on their members, and tend to be rather more rigorous, than the more casual, easy-believing, non-demanding, faith communities.
These are my impressions. Want to comment?