Pre-war Martins were built using Brazilian Rosewood for their back and sides, which is highly prized both for its look and its sound. But because it's so beautiful, it was also heavily used in the furniture industry as well (I've seen some enormous conference-room tables made of Brazilian Rosewood, and they knocked my socks off), and as a result it was over-farmed. So since WWII, the supply has been both rare and tightly controlled; as a result it's extremely expensive. In the late 1960's, Martin switched to using Indian Rosewood instead, which is very nice, but not as nice as the Brazilian variety.
You can still get guitars made with Brazilian Rosewood, usually from small, independent luthiers, but they're very expensive. Often times a luthier will offer Brazilian Rosewood as an upgrade option on a standard model, and I've seen the upgrade price as high as $1000.
Update: After having done some more research on Wikipedia, here's what I've been able to find out. Martin developed the dreadnought-style body shape around 1916, but didn't alter it to accommodate a 14-fret neck until 1931. Between 1931 and the war, apparently the craftsmanship was at its peak, especially when it came to carving the interior bracing. During the war, materials and skilled labor were both understandably in short supply, so the quality suffered a little bit. After the war (I found this bit interesting), the guitars slowly started to suffer intonation problems, apparently because due to higher production, the jigs used to position the bridge gradually eroded and no one noticed, until they did and fixed it.
So there are some other non-Brazilian-Rosewood-related reasons why pre-war Martins are preferred over post-war, pre-1969 Martins. But honestly, after having looked at a bunch of different sources, it seems as though the answer to the question "Why is a 1936 Martin preferred over a 1956 Martin, since they both used the same woods and design (and assuming no intonation issues)?" is basically "Because people liked the way they sounded and were willing to pay a premium for them." Which isn't exactly specific, and doesn't help you if you're wanting to re-create that magic with an independent luthier.