Understand, you were not even retaining the most recent compatible app versions between your two iPhones. Right there it should lead you to be extremely cautious about losing any data. Generally I don't advise folks to even try to move any data over w/ iCloud backups if the software/hardware versions are that drastically different. It simply leads to way too many errors IME.
Keep in mind that Gas Buddy and Next don't pull in the same type of revenue streams or have the same massive adoption/users numbers either as the other <much more predominant apps> you have listed. We cannot expect much as such from Gas Buddy, etc.
I got my iPhone 6S and am setting it up from a backup from my old iPhone 3GS. Just about everything worked fine. I noticed that some app data didn't transfer to the new phone. I use Next for budgeting and none of the data in the app transferred. Also I use Gas Cubby to track fuel and mileage data for my car. That data didn't transfer either. All the regular things like music, contacts, dropbox contents, etc... transferred just fine. Just wondering if this is the way some apps work? Any suggestions to deal with this?
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