The AntMiner S9i 13.5 TH/sec model requires 101.5 Amps DC. Since power (watts) is equal to voltage multiplied by amps, the total power consumed by the AntMiner is 1218 watts (+/- 10%). Note, this is regardless of whether that’s AC or DC, and regardless of voltage. 1218 watts is 1218 watts, or if you run it for an hour, 1.218 KW/hr. In my case, that works out to about $54.44 USD per month, regardless of voltage.
The APW3++ power supply doesn’t care what A/C voltage you supply it with, in the range of 100 to 240 volts, it simply converts that into the required amps output in DC. If the AntMiner is puling 1218 watts, that will translate (at 93% efficiency) to 11.85 amps at 110 volts, or 5.43 amps at 240 volts. Running two AntMiner S9s on a single 120 volt 15 amp circuit is pushing the boundaries of safe operation. You should ensure you only run a single AntMiner per 110 volt circuit, unless those circuits are fed with 12 gauge or lower wiring, and are rated for at least 20 amps.
Attaching the APW3++ power supplies to 240 volt circuits simply means you are pulling less amps per hour than if it is connected to a 120 volt circuit, and you can connect two, or possibly three, AntMiners to a single 240 volt circuit.
So, to answer your question, no, it’s not more expensive to run at 240 volts than 120 volts. In fact, due to power efficiency, it’s probably very slightly cheaper to run at 240 volts.