There is actually very little in common between the two products.
Monte Cook's
Arcana Unearthed is, essentially, an alternate PHB. There are new races (Faen, Litorian, Giants), new core classes (Unfettered, Totem Warrior, Magister), a new way of casting spells (I very much like the flexibility of the system), new equipment, etc. It also has repeats several "core" Feats, weapons, and the like -- many of these are things available in the SRD. This book could replace the PHB for some games, or serve as an adjunct in others.
WotC's
Unearthed Arcana is very different -- it is a series of alternate rules that could be plugged in, individually or en masse, to any D20 game. The usefullness of any individual rule is open to much personal taste and interpretation, but in many ways that is the point of the book; actually, including all the rules would be impossible, as several of them would contradict (or massively impact others). Example rules include a Wound/Vitality Point System, variant races and Bloodlines, and Reputations.
Which book you might choose would depend on the type of campaign you either are or are considering running.
Monte's
AU is good for a new campaign or for some interesting variants; most people take the book as the starting point for a campaign, therefore making the whole book useful. On the other hand there would be problem mixing the magic system from this volume with the core rules.
WotC's
UA is good for any campaign, but you will probably only use a small portion of the rules and material. Those rules, however, may make the difference between a campaign that feels almost right (using the Core Rules) and a campaign that feels Very Right (using variant rules from
UA).
Of the two, I have personally gotten more use out of Monte's book as I am using it to design a new campaign; many of the ideas in UA I had already found, in one variant or another, on the Net for free or had previously rejected for my own games. OTOH, you will find many, many people on this board who have gotten hordes of use out of UA -- besides it has that "official" cachet, which never hurts.
Hope this has been of some use to you
