It appears the limit is the maximum file size for iOS (logically), which is currently 4GB: https://discussions.apple.com/thread/1763096?tstart=0. The precise size of the data is circumscribed by the compiler types (NSData, NSString, etc.) or the files in your asset bundle.
I am sure there is low-level documentation on Swift types somewhere--but you will need to discover it yourself. :)
I have not redirected to another answer because similar questions also suggested that the limit is the device size.
Be aware that NSUserDefaults is considered harmful for large files, because all defaults are loaded immediately at application launch. Access time will be slow, performance will be impacted. Consider using a structured storage medium, such as Core Data, CloudKit, or SQLite, for large files.
https://developer.apple.com/library/mac/documentation/Cocoa/Conceptual/CoreData/nsfetchedresultscontroller.html#//apple_ref/doc/uid/TP40001075-CH8-SW1
https://developer.apple.com/icloud/
http://www.appcoda.com/sqlite-database-ios-app-tutorial/