PHP already provides a mechanism to replace errors with exceptions (set_error_handler() and the ErrorException exception type). I do this on all my projects.
Specific errors should throw specific exceptions. That way I can handle the ones I know how to handle and let the others bubble up and either completely break the app to be logged and fixed later or get handled correctly somewhere else. With ErrorException, you have to look at the contents of the error message to see if it's an error you can handle or need to rethrow.