As an avid devourer of both history and maps I can say that this book fills a certain niche within my appetite that has not been addressed by either thick historical reference materials or other historical atlases.
Specifically, the strength of this book (whatever its other failings are) is that it does the best job I've yet seen of presenting a TRULY DYNAMIC VIEW of the area in question. [For caveats as to its limitations, skip to the bottom of the review.]
This means that, after the early stuff is gotten out of the way (your neolithic revolution and other early times for which our information is sketchy, which involves leaving out a lot of time), we are treated to a map of the same area at regular ~50 year intervals. [The actual intervals between maps actually ranges from 15 to 100 in some cases, but ~50 is probably the mean.]
Now I own a few other historical atlases, many of which come highly recommended (The 2005 Oxford Atlas of World History, for example, as well as a few other comparable atlases), and while they are valuable purchases in their own right, they do not present a detailed DYNAMIC view of any part of the world, let alone sticking with one piece of it. The Oxford Atlas presents 'The Roman Empire' in two (admittedly large) pages that are supposed to take us from 500BC to 400AD, accompanied by three maps. While the simple narrative tells us what happens within that time period, we do not get to SEE what happens. Another atlas presents one very large and well detailed world map for every 250 year interval - empires pop up from nowhere like dandelions and are gone by the next map as if they never were!
In contrast, McEvedy's work sacrifices global scope and global time to present a limited frame of reference (Europe, North Africa, the Near East/Iran and half of the Eurasian steppe) and gives us a blow-by-blow account of what exactly was going on. We can actually see Rome growing over the course of 20 or so maps covering a thousand years, not to mention the ebb and flow of the various other historical peoples that shared the stage with Rome. [This doesn't take into account the pre-Rome maps that make up the other half of the book.]
I have yet to encounter any other series of maps, in proper historical reference materials or in other historical atlases, that provide this glimpse into a dynamic world that changed with each human generation (as all human communities do, whether we know it or not). [If anyone else knows of such a series of maps, by all means post a review listing the title.]
As an amateur scholar who prefers to get proper historical information from thick, specifically targeted thousand page works, I can definitely say that there is no substitute for the visual information that maps can provide. I've lost count of how many pages have been wasted attempting to explain in (many, many) words what could have been presented instantly and without confusion by a simple well drawn and well-excised map - in fact I've yet to encounter any proper historical work in which the use of maps has been what I'd call adequate. Every targeted proper history should have a section of dynamic maps as comprehensive in time (50 year snapshots) as McEvedy's work, and without all the clutter added in. [If the entire historical narrative never even mentions cities G-Z, why are cities G-Z included in the maps at all - to make cities A-F difficult to find?]
Finally, McEvedy certainly has a way with words, as well as a sense of humor, which makes the narrative, simple as it is, more enjoyable then your average millenium trudge.
Having said all this, however, one should keep in mind that this Atlas fills a specific and so far unmet need - without competition in that specific realm it stands unparalleled. When measured according to other parameters that are already serviced by other products, this Atlas is average at best.
Factors to consider:
1) Can only be classified as the most basic of introductions to history - the historical narrative is very very simple, easily outclassed by other atlases, and is primarily meant to simply accompany the maps and explain any apparent anomalies. This is not a book with which to learn history, but to offer a supplement to the amateur historian that simply isn't available elsewhere (at least not collected into one convenient place that I am aware of).
2) Limited in geographical scope. Relatively clearly stated at the outset. I, personally, would love to see the same treatment given to the rest of the world (either as a whole or by region or both), but this has not been attempted. [Cursory book store inspection of the regional Penguin Atlases, such as Africa or Egypt or Greece, suggest that they have moved away from the dynamic presentation of many maps towards a more narrative approach.]
3) Lack of detail. This is not a standard reference work - it is not a book with which to look up specific facts or places or cities. It details the movements of large numbers of people who are defined in cultural/linguistic terms - it is a work of demographic history, and in terms of such, excess detail would indeed simply get in the way of the purpose of THIS work. Other Atlases and dictionaries have already provided reference services.
4) The author is not precisely a neutral party. Whil McEvedy's specialization involves demographic history, in which I do not doubt he is both objective and an expert, he is not afraid to stake out a position on other issues in history about which he may not be such an expert. If certain historical controversies tend to set you off (such as the Aryan invasion conroversy), then you may well be set off by some of the random comments interspersed throughout the book. McEvedy's opinions clearly represent that backlash against the historical-PC movement (or whatever it might be called), in which there have never been any real Dark Ages anywhere at any time (as this would insult the people who lived at those times, making them seem inferior), and in which large regions were never invaded by other people (as this is a threat to the patriots of [Nation X], however long ago it didn't happen), or if they were invaded the 'invaders' were really friendly and nice and accomodating (not ambitious, opportunistic and clever thugs, because thugs are never smart), or that the invaders clearly made no useful or worthwhile contributions to subsequent cultural development (because aggression and invasion are wrong, and the perpetrators should not be encouraged by admitting that they were anything except pure destructive evil). Of course such theories began, some time ago, as a response to the old conservative position in which fresh blood and racial superiority demanded that invasions determined everything (because muscles are good), that the conquered people were weak, stupid, insipid and given to orgies and all manner of archaic and disgusting customs (and probably used masking tape to fix their glasses), that the conquerors were massive and virile noble savages (full of honor and repute and definitely not a collection of rapists and murderers), and that the conquered people were usually dissolved in the pure elixir of new blood (or at least kept where they belonged, in slavery).
Seen in the light of past and present exremisms, McEvedy's comments are pretty tame, and more of a calling for balance between various hypotheses (which, when left to themselves, tend to become hyperbolic). In any case such few comments as exist are not integral to any theory presented by McEvedy, and are really no more than asides to the work - most authors would excise such unnecessary and provocative comments, but McEvedy has not. The comments are almost meaningless to the purpose of the book, so you can easily take the maps and forget the narrative completely, and still come out ahead, regardless of your position.
In summary, and speaking as an amateur historian, this book is an amazing kind of supplement that I have yet find anywhere else. It is not, however, a comprehensive introduction to world (or regional) history, and it is not a general reference work.