I bought both books at the same time, and I think I found a useful comparison. Let's think Food Network.
Designing Great Beers can be compared to Good Eats, and I would compare Brewing Classic Styles to Tyler's Ultimate. Naturally, if you are not a fan, the reference means nothing, so I will try to explain myself a bit.
Alton's show, Good Eats, dives so far into the science and history of food and cooking, you may miss the recipes as he covers them. An earlier poster described Daniels book as "intense"; a more perfect description does not exist. I love Good Eats, but I love and understand food and cooking. My cooking is at a point where I can go beyond the recipes, and I want to know "why", and Alton provides me with the answers. Further, I believe that Jamil took a lot of inspiration from Daniels as he formulated recipes, so you actually pick up a lot of similar information by cutting through a lot of the fat that personally, I was not ready for.
Tyler's Ultimate featured Tyler Florence traveling the globe and piecing together the best aspects of several recipes and techniques, essentially, forming the "ultimate" recipe. Jamil's book nails this concept. For the most part, his recipes define their styles (he pretty much writes the BJCP guidelines) and they are proven. I am not at the point as a brewer where I can identify hops and grains the way I can identify herbs and spices, so I need Jamil's book for help. His recipes will be better than mine everytime, because they have been tested, tweaked, and improved. He also has an example and description for EVERY style. Generally, it is a page or two dedicated to the process and style, and a page for the recipe. Daniels goes on for 20 pages about British Bitters and Pale Ales, but many specific styles are not even mentioned.
To sum up, if you want to know "why", go with Daniels book, if you want to skip to "how", go with Jamil's. Personally, I lean toward Brewing Classic Styles.