This old request is now [status-completed], but it was not implemented in the way proposed, with the ability to subscribe to specific answers and comment threads. I'm proposing to move it back into the [status-planned] stage.
The new favorite notification logic is not good enough. Both because it conflates two things, and is not fine-grained enough. I may want to favorite a question without being notified about its changes, but that option does not exist.
For example, the question "what is the best programming book" is worth saving as a favorite, but it changes too rapidly to subscribe to all its changes. Some users want favorite notifications turned off because it is too noisy.
There is no middle-ground between "all" and "none".
It also forces me to see changes to everything on a favorite question. Often I only care about changes to one answer, or changes on the question itself (its content or its comments) but not any of the answers. Again, no middle-ground.
For these reasons, I do not feel that sending notifications on all favorited questions is the right approach. There should be a way to request from the system specifically the notifications you want to see.