I think it depends upon the use cases of the API, but if you want someone to be able to build snappy and fast "apps" using your API rather than just facilitating movement of data in/out for an integration with another piece of software, I think granularity is important.

Having built our front end using AngularJS, we are the first users of our own API and that has driven it's design. In order to make things quick, we really needed to trim down response payloads in some cases which kind of deviates from standard CRUD patterns in some areas.

This has come at the expense of good documentation (we have a lot more methods now and having good examples of all of them will be expensive) and consistency--things are not very uniform anymore. However, as an API consumer I'd rather have the API give me too many options rather than too little. Our API has gone from "pretty" to "very functional".