There isn't really any difference; a class cluster is a specific implementation of the Factory pattern. In the class cluster, the initialiser is used as the factory method to decide what instance to return.
Stylistically, the class cluster will be familiar to users of your API because it's common in the Apple frameworks: the collection classes, number classes and others make use of the pattern. It also satisfies the higher-level pattern of Smalltalk and Objective-C where the class object is itself a factory for its instances.
In addition the class cluster means fewer things to remember: rather than thinking "I have to make a
ThingFactory then call
[factory thingForCase: foo]" they just look at the initialiser for
Thing, which is what you'd probably reach for by default.
There is a situation in which you would reach for a more "classic" implementation of Factory, which is (as discussed in the comment thread) where the objects you might return won't necessarily be subclasses of a common parent. In the class cluster pattern, there's a common superclass and client code treats whatever object is returned as an instance of that superclass. If this restriction in the type hierarchy is not suited to your case then a class cluster is not going to work.