The difference is religious people seem to need their religion. If they were confronted with proof that their God isn't real I think a lot of them would be very broken on a spiritual and emotional level.
That which is not physical is not able be proven nor disproven because it is not of the physical realm. The second part is interesting. How many people do you imagine are already broken on a spiritual and emotional level? Are you imagining many of these would be spiritually and emotionally healed if they took up religion? The reason I ask is it seems you already accept there is power in having faith in God? I find that interesting.
Some of my family members were/are atheists; I am married to an atheist. While this is a small sample, there is one thing I notice between family members who are atheists and those who have faith. 'My' atheists have expectations of God and what He can do and those expectations are not met. They tested God and He failed. Think about this for a moment because the Commandment states,
You shall not test the Lord your God. It is an interesting Commandment. To me it is a heads up that in seeking God, testing Him is a sure way to fail in finding Him.
People of faith seek God, get to know Him both by what He does do and what He does not do. We have the Bible from ancient times that note people's experiences with God. In modern times we have accounts of near death experiences, experiences with both angels and with God, visions of Mary. What people of faith mostly have is the Spirit working with their own spirit to make the best version of oneself and also be a guide through our personal life.
My advice for those truly interested in God is to seek Him without testing Him. The stories of others' experience (both great and small) are interesting and encouraging. But they don't hold a candle to what one's own story and experiences can be.