The reason to use a factory instead of 'new' is that a factory can vary the return type, unlike a plain constructor. You need a factory when, based on the constructor parameters or the system configuration, different classes of object may be instantiated. I really have to disagree with your characterization of the GoF book. The premise is that it's a set of designs that can be applied when specific situations are encountered, though, granted, if you're reading the book before you've actually seen the situation where a particular pattern can be applied, it seems abstract. Certainly, popular conceptions of patterns taken out of context make that problem worse.
You could do that more or less in Javascript by creating and initializing different member variables in the constructor depending on a constructor argument but I would hate you for it.
yeah, they say in the introduction even that it is to give a language to common patterns that emerge in C++ style OOP. It gives examples of what it might look like, but isn't an instruction manual on what to do. Its to give a common language "this is a gateway" as opposed to "this is where stuff goes in", or "front-door" or whatever tribal names / descriptions people come up with.
