Voltage can't drop faster on the 7 because you can't have (much of) a potential difference across a conductor. The 7 Ah battery would need to be at a lower voltage than the 14 Ah battery and... well, how would that happen? In practice, the batteries are discharged in a rate proportional to their capacity, so the 14 Ah battery would provide 2/3rds of all current, and the 7 Ah would give 1/3rd.

If they're in parallel, the capacities will add and they'll always be at the same state of charge.

There are exceptions to this in extreme cases (where internal resistance becomes an issue) but I can't see you hauling over a hundred amps out of these things if all they are is a UPS.