You'll need to migrate a copy of the iCloud data on one of the phones to a separate iCloud account using a different Apple ID, then manually delete the data you don't want from each account.
To migrate to a new account, start by saving any photo stream photos you wish to keep to your camera roll (unless already there) by opening your my photo stream album, tapping Select, tap the photos, tap the share icon (box with upward pointing arrow), then tap Save to Camera Roll. If you are syncing notes with iCloud, you'll need to open each of your notes and email them to yourself so you can later copy and paste the text into new notes created in your new account. Then go to Settings>iCloud, tap Delete Account (which only deletes it from this device, not from iCloud and won't effect the other phone), choose Keep on My iPhone and provide the password to turn off Find My iPhone. Then sign back in with a different Apple ID to create the new account and choose Merge to upload the data.
Then you can go to icloud.com from your computer and manually delete the unwanted data from each account.
They can continue to share the same ID for iTuens without any problem. However they should use separate IDs for FaceTime and iMessage (to avoid getting each other's FaceTime calls and text messages). On the phone that was migrated to the new account, go to Settings>Messages>Send & Receive, tap the ID, sign out, then sign back in with the separate ID. Then do the same thing in Settings>FaceTime.