The writing styles are different, but in terms of contents they are similar so it's difficult to say. It depends on your background etc. For example, even though Shreve is very comprehensive and well written, I much prefer Baxter&Rennie for an introductory book (Shreve is a bit more mathematically detailed, but that I feels bogs down the presentation).
So with that preface, personally I would say I prefer the style of Andersen&Piterbarg, but it can be a bit encyclopedic. Also, the book is to my mind clearly written for practicing desk quants (or those aspiring to that role), rather than as an academic exposition. Indeed there are sections there that only practitioners and model implementors would care about, such as numerical methods for PDEs and Monte Carlo (in Vol 1). As I remember it, Brigo&Mercurio doesn't have chapters on those (but it does have that appendix on "talking to traders"). B&M has a lighter writing style with jokes about DC Comics and so on.
Well I love DC comics!!
But then though I am not a desk Quant, but as a Model Validation Quant as well having a good grasp on Numerical Techniques and MC Simulation is highly required.
Thanks