I think it's a matter of theme. If you want to underline the apocalyptic theme, start hacking AW until you get to Dark Sun. If you want to underline the fantasy theme, start with DW and add apocalyptica.
Both approaches have their strengths and weaknesses. If you start with AW, you have to basically re-iterate the whole process of DW to come up with races and classes. If you start with DW, you have to add apocalyptica. But you could follow in the footsteps of the original Dark Sun boxed set.
The design question is: what seems to be easier? Or just take AW and DW and produce their love child: Dungeon Apocalypse.
The core of the game are the playbooks. With DW, you already have those. With AW, you have to start from scratch. But AW describes the necessities of apocalypse fronts better. So, I would go with both.