I miss the "good old" inventory, oil management and sanity meter. They were big *gameplay* parts of TDD. I had things to do and to think about instead of, you know, just walking forward. TDD had exploration, involve some thinking of the player not only about the story, but also from the puzzles too (which were, mostly, just right in the first game IMO).
At this rate, next game will what, a slide show?
(just kidding here)
I also miss deeply the physics affectting all objects in the game world. It is huge for me. It harkens back to the concept of immersive simulators. In TDD the physics was consistent, it helped me believe I was in a consistently logical world despite all the supernatural things going on. Helps gives a sense of immersion, of "reality". In AMFP it just shows the Game Designer Hand, just show how artificial the world is: If the all powerfull Game Designer wants, I can move this object, if he does not want, I cannot. Thus, it less believable game world for me.
If only AMFP managed to be scarier, people would be more forgiven of if. But it simply wasn't. If anything, it felt more scripted for me. I could see most scares coming a mile away.
One great thing AAMFP did, that as far as I've read is not mentioned at all in "big" magazines/sites review, is the fascinating subtlety of the changes in the game world since the very beginning (maybe because they are very easy to overlook). Pig mask appearing/changing, one mask that is visible when looking behind a painting but not when you are physically in the room, the owl statue that goes to the other side of the "hunting" room and more. This was really a high point of the game for me.
The story is thought provoking, kept me hooked (though looking back, all things considered it does steer towards melodrama a bit too much).