I have seen many examples where a view-controller is initialized using its storyboard-ID in Main.storyboard:
UIPageViewController *myPageViewController = [storyboard instantiateViewControllerWithIdentifier:@"PageViewControllerID"];
Are there any particular advantages of doing it like this instead of just doing the old alloc-init?
If you choose to use a storyboard then you either request the initial view controller (or allow the system to do it), request the view controller by identifier or trigger a segue. The advantage of requesting by identifier is that you can do whatever you want with the controller. Segues are much more powerful than they used to be and basically everything can now be done directly, but there could be some conditional logic you'd rather run (which could trigger a number of segues...).
You don't need to use a storyboard though. If you want you can create everything in code or you can continue to use NIB files. Storyboards help when you're using auto-layout and want to take advantage of the layout guides. 99% of the time using a storyboard will save you time over using just code and perhaps 50% of the time over using a NIB.