Should I use the book that is recommended by the professor?
You would probably just be making additional work for yourself by using a different book, even if it is superior. That doesn't mean that you shouldn't do one thing or another, just be prepared for the extra work that might be implied. This might be especially true for exam preparation. 

Some professors will ask students to read a section of the text before a lecture so that they are prepared for what will be said. Usually this would be by chapter/section rather than by named topic. 

But, if you have the option to speak to the professor you could ask him this question, mentioning the other proposed book(s) and getting his advice. Perhaps he will tell you why it is ok or not ok. Perhaps there is some feature of the suggest book that he will be especially dependent on for the course.