Very important this one.

I think it also heavily depends on whether the mobile app and the server side are complinentary, inter-dependent, or redundant.

For example if your web service was a way of managing say, your stamp collection and your app was just a way to browse it offline; that would be a lot worse than if your app was a standalone game, and the server side was just a way for people to list their high scores in public.

But, obviously some people are going to be mad anyway, since they had some expectations that you will no longer be meeting.