I thought one of the reasons that backups are small is that they contain pointers rather than the actual app. In a restore, the pointers are used to download the app from the store....which I think would give the latest version.
I think the above is probably true for restoring from an iCloud backup and may also be true for an iTunes backup.
One reason I say this is that after the last iTunes restore I did, I got a message that some apps were no longer available on the App Store, implying it tried to download them but couldn't.
If you still have the old app file I believe there are ways of restoring/installing it but I haven't done this.