I'm just about finished with chapter 1 of the alg/trig book. I can compare it only to a book of the same title written years ago by Rees & Sparks which I worked most of the way through. Axler's book requires a lot more thought than the other one! The odd-numbered exercises are solved by the author, which provides continuity with the text material. After the exercises there are problems, some of which are the 'show that' type; some of these are quite interesting (read challenging for yours truly), none of which have solutions, which is fine with me. At the end of the chapter there are review questions, also with no solutions. The book is about 750 pages, which is quite a bit smaller than some of the other mainstream offerings, especially given the full solutions to the odd exercises. The precalc book is about 600 pages and I did a cross-reference of the tables of contents as best I could and I would say that everything in the precalc book is in the alg/trig book. The alg/trig book seems to have more exercises per each section and it also has a bit more trigonometry and about 60 pages on systems of equations, most of which is not in the other book. Matrices and matrix algebra are there, but I don't see anything on determinants.
The exercises in chapter 1 introduce the Greek letter epsilon in a problem with absolute values, inequalities, sets, and intervals; seems like precalculus to me!