My pick would be The Assassini by Thomas Gifford. I didn't pick this book up because I'm a Dan Brown fan or anything, but because I was really into the Assassin's Creed series of games by Ubisoft and wanted to read something along those lines. My copy of The Assassini had a blurb on the cover that the book is a conspiracy thriller "as shocking as The Da Vinci Code" so it should be a good match for your taste. The story is about a secret society who are in control of murdering anyone who seek to uncover the deepest secrets of the church. This brotherhood of killers used to protect the Church back in ancient times, but nobody knew that they were still very active and still doing their jobs. A lawyer called Ben Driskill uncovers their existence when he investigates the death of his sister, who was a nun. Since the church appears to have no interest in uncovering who the killer of the nun was due to her being a bit of an activist, Ben takes matters into his own hands. The book didn't quite scratch my itch for Assassins Creed style action, but if you liked The Da Vinci Code I suppose you'll enjoy The Assassini.

Just take a look at all the books that were released shortly after The Da Vinci Code to cash in and you'll find a lot of similar ones! In all seriousness though, I actually enjoyed a book by John Case called The Genesis Code. The protagonist is a revenge driven ex-FBI guy called Joe Lassiter. The cause is the death of his sister and nephew at the hands of some religious nuts. Joe keeps digging until he discovers that the Vatican is somehow involved in the murders in an attempt to cover up something that they want to keep buried. It begins with Joe wanting to get revenge for the death of his sister, but spirals into a whole conspiracy theory that stretches across the globe. The Genesis Code is one of those kind of far fetched books that are nonetheless entertaining to read on a long flight, which is exactly how I would classify The Da Vinci Code.