One key difference of Designing Great Beers and Brewing Classic Styles is that Designing Great Beers focuses on the history of the beer style and historic creation of the beers, followed by a synopsis of what brewers of circa 2000 are doing to create beers of that style. It leaves out personal opinion, and focuses on historic literature and "modern day" recipe formulations WITHOUT actually giving you a recipe.
While Brewing Classic Styles gives a quick synopsis of a beer style, it is very much influenced by Jamil's personal opinion and brewing preferences followed by an actual recipe formulated by Jamil. After listening and reading a lot of Jamil delivers, I recognize that he has specific assumption and preferences that differ from classic brewing practices. This isn't a bad thing, just something I'm aware of when reading/listening to Jamil - I take his recommendations with plenty of salt. I like BCS on the whole and it complements DGB very well, but if I had to recommend one book to buy it would be DGB (followed by Brew Like a Monk

since DGB doesn't touch on Belgian beers).
The two books take a difference approach at presenting stylistic traits of various beers. One gives you a detailed breakdown of a beer style leaving it up to you to "go forth and formulate a recipe" while the other gives you a quick synopsis of a beer style followed by a recipe from the author. I am more favorable to historic description followed by the thought process of formulating my own recipe than I am being given a recipe to try.
Aside from that, in regard to DGB being outdated, when we're talking about classic beer styles and giving the historic background of them it's
never outdated - it's exactly how it was done historically speaking. Even the commercial and homebrew ingredient breakdown is still very relevant to today's brewing practices. While Part 1 of the book is definitely long-in-the-tooth, it gives a nice breakdown of how a modern brewing software calculates the values it does. It was worth reading once through to get an idea, but
it's Part 2 where the book becomes invaluable. The only aspect of Part 2 that is a bit dated would be the hop selection presented for most American styles since many were not available when the book was written (i.e. amarillo, citra, simcoe, etc, etc); however the hop selection for most european beer styles remains relevant today.