I have exactly the same problem.
In the Calendar Prefs on a Mac running Mavericks, one can select "Show Holidays calendar" in the "General" tab. But this setting is seemingly only for the local Mac. One can use the Info panel of Mavericks Calendar.app to move this subscribed Calendar to an iCloud account, and then it sync's to other Macs/iPhones, but NOT to iCloud.com.
However, all these actions DO NOT affect the Holiday Calendar on the iPhone. For this one, one can only chose between show and do-not-show.
Result: as long as one has not all devices that one is syncing running Mavericks, it seems one will have a duplicated Holidays Calendar on the iOS 7.x devices.
ADDED: on Mavericks Calendar.app I can rename the Holiday Calendar, but this is not possible on the iPhone. Also, it seems that a color selected for the Holiday Calendar in Mavericks Calendar.app (and also a changed name) will not sync to the iPhone.