For years, I've used the Peterson field guides to identify birds. Most of my bird watching has taken place in the Eastern U.S. mountains and north and south of the coastal area where I live, as well as WI (summer) and LA (winter). The Petersen guide book for the Eastern region meets most of my needs, but I also own several other books (Smithsonian and Audubon). I became interested in the National Geographic book BIRDS OF NORTH AMERICA because I admire the NG magazine.
The NG is a heavier book than the Eastern Peterson, perhaps because it shows birds from both the Eastern and Western areas of the country, but the Peterson maps show the full range of "Eastern" birds--even if a range extends to the West. Both books show ranges that extend into Canada. The NG book is nifty because the little maps that appear in the back of the Petersen books are on the same page as the bird illustrations.
The birds illustrated in both books are clustered by category. For example, Petersen shows male and female Downey, Hairy, Northern Three-toed, and Black-backed woodpeckers together, as does the NG. The Petersen guide has little arrows that point to distinguishing marks, but NG does not. I find these indicator arrows very helpful when I am trying to tell two closely marked birds apart. The NG does show a tiny row of variants across the bottom of the page (For example, the woodpecker page = fasciatus, dosalis, orius, etc.)
The bird colors are less differentiated in the Peterson than the NG illustrations. For example, stripes on the Peterson Three-toed woodpecker's belly are less articulated than those shown on the NG bird. I don't think this matters as one seldom gets close enough to see the mottling. The Peterson birds are hand drawn and relatively flat, while the NG birds are more rounded, i.e. modeled. The Petersen birds look like the Audubon paintings. The NG illustrations remind me of digital photos of taxidermist stuffed birds (probably why the colors are so differentiated).
Both books provide measurements and Latin names. The Peterson book provides text that describes birds that might prove confusing with your bird of interest. The NG book provides text that describes the attributes of regional variants. This latter feature won't help you in the field since you almost never see regional variants in the same location.
If you are a serious bird watcher you will probably want both books and the Audubon and Smithsonian books as well. If you can only afford one book, I recommend the Peterson book. I have used my Peterson book for so long it just falls open when I hold it in one hand, so I am probably prejudiced.