For example one major difference I've noticed is iCloud can sync while asleep (Power Nap). This has proven to be very useful with my iCloud Photo Library, which has tons of syncing to do every day and night over a slow connection.
Another distinction with Apple's approach, maybe not directly comparable to Dropbox Business, is how it is integrated with apps. I mentioned photos, but it also covers iTunes music and movies/TV. It lets it be smarter than a purely filesystem level sync, like downloading photo previews and purging movies only after you've watched them. In other words it has a direct Dropbox competitor in iCloud Drive, but also adds domain-specific syncing.
Are there any advantages to Dropbox's approach?