Custom Exceptions: Differentiate via many subclasses or single class backed with enum?

I'm looking to implement my own set of Exceptions for a projects I am currently working on. The project relies on a core framework with a base framework exception MyFrameworkException (I am also writing this framework).

For any given project I would like to throw several different types of Exceptions and I can't decide between using multiple subclasses or a single subclass with some form of an Enum as a constructor parameter.

In both cases I have:

public class MyFrameworkException   extends Exception              { /*...*/ }

Option 1:

public class MyProjectBaseException extends MyFrameworkException   { /*...*/ }
public class SpecificExceptionType1 extends MyProjectBaseException { /*...*/ }
public class SpecificExceptionType1 extends MyProjectBaseException { /*...*/ }
public class SpecificExceptionType1 extends MyProjectBaseException { /*...*/ }

Then, throughout the project I would throw the specific exception for any problem that occurs.

Option 2:

public class MyProjectException extends MyFrameworkException {
  public static enum Type {
    SpecificType1, SpecificType2, SpecificType3
  }
  public MyProjectException( Type type ) { /*...*/ }
}

Here I would always throw MyProjectException with the specific enum type for any problem that occurs. I'd provide some mechanism so that a switch statement could be performed on any MyProjectException based on the type enum.

What's the best way to handle exceptions in projects, especially those sharing a common infrastructure? Are the two options above good solutions? Why or why not? And what are any better solutions?