I am interested in studying Computer Science Theory for the Information Age by Hopcrot and Kanaan[0]. How do these books compare? Is there much overlap between the two? Are they totally different?
Very different. Their text focuses on the connections between stochastic systems, information theory, and machine learning/discrete models in mathematics, whereas the one you linked is purely about statistics and machine learning from a classical perspective.
btw, you've linked to a 2012 version of the book. Since 2012, they've added another author and changed the name of the book. I have no idea how much the content changed.