The two books are quite different in the language and formalism used: more formal and mathematical inclined AHU with respect to CLR. I'd say, the very classic style of his authors who have made history in the CS literature with their books (particularly 2 on algorithms and data structures, 2 on Computer Theory, 2 on Compilers, 1 on CS foundations): as these books have been used in most universities around the world for decades, they've proved to be real milestones in the education of thousands of students.

The books differ also in scope, since AHU is certainly not an encyclopedic collection as CLR does, with his roughly 500 pages against 1000. In spite of this, I'd point out the following: my textbook on Algorithms was CLR, but when we got to Complexity Classes (P-NP and theory behind) we "had" to switch to AHU for the simple reason that CLR did not almost mention at all Turing Machines nor Space Complexity, without which is certainly possible to learn e.g. about NP-TIME completeness, but without which, such a path would equally certainly miss some foundamental topics of Complexity Theory.

All in all, then, imo the book truly deserves 5 stars (and perhaps it would deserve a second, updated, edition too ... possibly, imho, through a bit less revolutionary revision job than they did with "Introduction to Automata Theory, Language and Computation").

As a final note, those looking for a more applicative and self-reference than an educational introductory text, could have a look at the two-volumes opera by the former Knuth's pupil, Robert Sedgewick (possibly the more consolidated C or C++ versions).