When Apple came out with Storyboards in Xcode, I thought that they would be quite useful in making it easier to see how an app was laid out. However, after attempting one project with them, I determined that they had limited utility as they wouldn't scale and wouldn't work well for multi person teams. I left storyboards for a year and didn't revisit them.
I started another project about a year after my first experience and decided to give it another go. This project was a small project and I was the only developer, so it was well suited for storyboards. The project grew and grew. Storyboards worked OK, but the layout in Interface Builder was almost too hard to manage. I finally decided to see about splitting up the storyboards into multiple storyboards.
The app was a tab bar based app, so the logical breakdown was one storyboard per tab. It only took about 15 minutes for me to do this and undo a poor initial decision. However, there were still one or two links between storyboards that were easy to fix in code. Some peopl have come up with ways to link storyboards like RBStoryboardLink which looks interesting, but I haven't explored it.
Multiple storyboards seems scary at first, but it is worth doing to keep difference parts of an app more contained and easier to visualize.
I haven't used XIBs in about a year and I'm not sure there is a good reason to use them as storyboards are easy to work with and make it simple to use custom UITableViewCells and UICollectionViewCells.