To figure this out, you need to make a distinction between protestant churches (think of the large mainline denominations) and evangelical churchs (Baptist, independent, and fundamentalist denominations).
The truth is mainline protestant churches are also losing members at a huge rate. Evangelcal chruches, on the other hand, have been growing at a rapid pace. The serious churches are gowing, while the lukewarm churches are shrinking.
I suspect if you apply that same logic to the Catholic church, you'll find that the churches that are preaching a lukewarm message are shrinking, while those that are standing firm on doctrine are growing.
In other words, this isn't a protestant vs. Catholic issue, it is a liberal vs. conservative issue. The liberal wings of both protestants and Catholics is shrinking, while the conservative wing of both is growing.
Given that assumption, it's easy to see how someone attending a liberal (lukewarm) Catholic church could be attracted to a conservative evangelical church, or that someone attending a liberal (lukewarm) protestant church could be attracted to a conservative Catholic church.
“The serious churches are gowing, while the lukewarm churches are shrinking. “
I am not a RC and won’t defend them but I take issue with that statement. Mormonism is the fastest growing church in the U.S. any many of these other “growing” churches are independent/charismatic that have there own issues such as the prosperity gospel heresy. I don’t think numbers explains what is going on in the U.S.