The Longman Pronouncing Dictionary is in competition with the "Cambridge English Pronouncing Dictionary" and the "Oxford Dictionary of Pronunciation for Current English". These dictionaries share many features (e.g. all of them give both British and American pronunciation and provide transcriptions for inflectional endings), but of the three, Longman is easily the most comprehensive and sophisticated one. It indicates whether an alternative pronunciation is simply a possible form within RP, a non-RP form or whether it is derived by rule (e.g. assimilation), it provides native pronunciations for loanwords and, most importantly in my view, it gives concrete percentages (with graphs) for many words that have two or more possible pronunciations or stress patterns (e.g. is "exit" pronounced with [s] or [z]?). This wealth of information, of course, makes the Longman dictionary slightly more complicated to read than the two other dictionaries, and you have to know a few more symbols to use it. Thus, it may be less suitable for the general public. But if you are a language professional (teacher, researcher, student, newsreader etc.), you will probably find these extras very helpful.
All in all, therefore, this carefully composed work by John Wells is the best choice for those who appreciate a little more detail.