No problems whatsoever.
The real problem lies with the possibility of my Calendar (which is always updated via my iPhone) no longer syncing with my wife's and vice-versa. Same with PhotoStream. When you have a little one and are taking tons of pics, it's nice for those pics to automatically appear on everyone else's phone with no extra steps.
Perhaps I'll wait for the iPhone 5S/iPhone 6/iOS 7 announcement. If there's not a 5" screen on it this year, I'm out.
If you guys were to share a dropbox account, you could use that instead of photostream. The s4 would automatically upload the photos like photostream and the iphone would upload once you launch the app. For calenders there is a way to still use the "cloud" calendar. I am not 100% sure of the app name, but it is all over these forums.....maybe like smoothsync or something similar.