These two books take a fundamentally different approach to delivering material to you. The creative input into Bills book is essentially from Bill, the Wrox book is from a team of 19 contributors. The Wrox book goes into almost excessive detail, if you want to be sure you have something like the ultimate in depth tome then this could be the book for you. However the saying about not seeing the wood for the trees can spring to mind. Bills book has the benefit of a single coherent voice and he concentrates on the essentials right from the start. Bills book comes with a CD, the Wrox book does not. However you can of course download all the material for the Wrox book from the Wrox web site, a site well worth putting in your bookmark list for its general java Material.
Bill Brogden has been involved with Java since version 1 and I came to know of him through his writings on Java Certification. I have read Bills book from cover to cover, every word, and was impressed with the accuracy of the text. With the Wrox book covering 1,600 pages and a much wider range of topics I didn't read everything, but took a good look at the topics I am interested in. Bill tends to put only code snippets in the text whereas the Wrox book has much larger chunks of code, even to the point of entire programs. Some people will think this unnecessary as they can read the downloaded source code. Other people consider reading code onscreen a horrible experience and it's an option not available when you are sitting on a bus, you decide.
To illustrate how the Wrox book takes the opportunity to cover all possibilities appendix E covers a technology called Swing HTML generation. I consider this to be a rather off-beat technology that will not attain widespread use as there are other more widely adopted solutions. On the other hand, to take another example the Wrox book has a 50 page chapter on the JavaMail API. Many web sites need the ability to send emails and JavaMail is both an easy and essential technology. As you would assume from a book that mentions J2EE the wrox book goes into details on EJB technology including a 45 page chapter based on the EJB2.0 specification. I got the feeling when reading this chapter that the authors had actually used the technology "in anger" rather than simply reading the documentation and putting together some test programs.
If you want the ultimate in-depth detailed guide it is no contest. The Wrox book is one of the biggest, fattest reddest, most in-depth book you can buy. Some people like more concise books, they feel that the job of an author is to sort out and present the essential bits. Bills book is probably better if you are relativly new to the subject. If you want a concise book that you can easily pick up with one hand, can be read from cover to cover by a reasonable person, is cheaper, comes with a CD and is very accurate, Mr Brogdens text fits the bill.
Concise, accurate, affordable
Depth, breadth,completeness =>Wrox