So, the big question: "Do you need to play Alan Wake before you play the AWE DLC?"
If you have any inkling to play Alan Wake in the future, I'd say play that first (and don't forget the two DLCs). Otherwise, you'll spoil that game's story (even more than base game Control already has), and really have no reason to go back. American Nightmare isn't entirely essential, but I think its (barebones) story gives you an idea of how the series will continue.
If you don't plan on playing the original 2010 Alan Wake game, then you can jump right into AWE, as most of the story of Alan Wake is recapped in files & tapes found throughout the DLC.
The environment is lot more like the base game than the Foundation DLC was.
Unfortunately, the bulk of the AWE DLC is just the same "remember that guy from Alan Wake?" boss fight recycled 5 times (with the final fight being stupidly frustrating, due to the boss' ability to heal way-too-fast). Luckily, you can adjust some new difficulty sliders introduced with this DLC to deal with this ridiculously bullet-spongy final boss fight.
There are also a few uninspired checklist side quests (clear 3 mold rooms, clear 3 gunk -- I mean "darkness" -- rooms, etc).
Alan Wake himself's Hotline appearances are just a bunch of gibberish dialogue and really don't add much to the add-on. The whole DLC really feels like filler for a quick "something is happening in Bright Falls in a couple years" Alan Wake 2 teaser at the end.