Although I don't own any of the alternative 'complete works' publications (I have also heard, for example, good things said about the RSC complete works edition) for me at least, this Oxford edition is simply an essential part of any fans library. Indeed, it's a great version for anybody who may be studying Shakespeare, but is not full of 'study notes' at the bottom of every page (which I don't like). Instead what we have here is the truly complete (as far as we know at least) canon of the Bard's works. They are presented in a form that is as close to what Shakespeare intended them to be, as is possible to get (at least to our understanding).
Before each play, there is a brief (one page) background introducing the context of the play, and what we know of its performance history, how it was received by critics and audiences, as well as the editors own justifications for having presented the play in such a way that either incorporates, or omits, elements from previous publications (mainly from the good or bad quartos and folios). It's also a real treat to have, for the first time, two different versions of King Lear reproduced in here (purely because we don't know which version in the 'definitive' one).
I own the first edition of this (published back in 1986 or '87 I think) but I have to say I believe this second edition really does surpass it. Not only do you now get more, but you also have, by way of introduction to the volume, a very detailed account of why new things have been included, as well as any reassessments which have been made of the works since 1987.
In conclusion then, a real gem, and a must have for anybody who was ever into Shakespeare, or indeed literature and the English language in general. I can't recommend it highly enough!