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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?

[0] https://www.cs.cmu.edu/~venkatg/teaching/CStheory-infoage/ho... (PDF)

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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.

Anyway, here's the latest version of the book: http://www.cs.cornell.edu/jeh/book2016June9.pdf . (I got the link from http://www.cs.cornell.edu/jeh/)

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