1. The Spurs have been better in the draft. Danny is very good but the Spurs are just outstanding at spotting talent particularly late in the draft. Ginobili, Parker, Splitter, Leonard, Blair...etc.
2. The Spurs, like LooseCannon said, are good at not over-shooting with supporting players and just finding good solid role-player types. (I think more safe choices and fewer swinging-for-the-fence types like Shaq, JO etc. would have made us better off).
3. They assembled their "Big Three" much earlier on, so those guys have played together longer and are still playing at a higher level than ours.
Only #2 is something you can lay at Danny's feet, I think, in terms of running the organization. We've done well in the draft, and expecting Spurs-level success is just too much IMO.
And, the Spurs got to draft Tim Duncan as a rookie...Danny had to build his team from a much lower talent base. In some ways that's just as impressive.