Will battery last longer with larger capacity but lower efficiency (high V through LDO) or vice versa?
LDO regulators don't "transform" energy, they are "linear" regulators. Whichever goes into the load, nearly the same current will be drawn from the battery.

So, within conditions of your task, the largest battery has 5 A-h capacity, the medium one has 1.7 A-h, and the smallest one has 0.6 A-h.

Since the same current (0.028 A) will be consumed from a battery in all cases, the run time will be 178 hours (5/0.028), 60.7 hours, and 21.4 hours correspondingly. I assume that regulators have negligible control losses (quiescent current) in their feedback/control circuitry. If not, this "control current" needs to be added to the 0.028 A load. 

ADDITION: MCP1700 uses MOSFET as regulating element, with control circuitry consuming a negligible 1.6 uA (max 4 uA) additional current from input. For LM2931 the "ON" current is 2.5 mA typical, up to 30 mA, so LM2931 might last half of MCP1700 time. True, the MCP1700 can't handle input voltages above 6V, but there must be other low-quiescent-current regulators. And, as Tony Stewart hints, DC-DC switching converters would do a much better job.