Some info:
The vast majority of Christians in history (over almost 2,000 years) were illiterate. That's part of the reason why stained glass and other church art was developed - to visually teach the stories and concepts to people who couldn't read. It's not required for Christians to read through the Bible. The Bible is not the point of the religion - your faith, belief, virtuous conduct and practice of the rites is what matters. The idea all Christians must read the Bible and everything rests on that is a Protestant idea. It's foreign to Catholicism and Orthodoxy. Catholic and Orthodox Christians are still encouraged to read it on their own, though.
As for Muslims, almost half of them are illiterate these days and most of them don't read Arabic, especially the classical Arabic of the Qur'an, which is considered the only authentic version of it. So, no - they're not reading the Qur'an as much as thought.