There isn't any difference in this case, but only because it's prefixed with:
var obj = ...
Without that, only the first version is correct, because you need the additional parentheses to allow the interpreter to correctly parse the function as a function expression and not as a function declaration.
You would of course only omit var obj if you only want the function to run (i.e. you want its side effects) but it either returns no value, or you don't care what its return value is.