If they have identical cooling capacity there is no real difference.

Given the circumstances as described, I would choose the 240 volt unit. In event of a power brownout, the 240 volt unit might handle it better. And any conductor has voltage drop when in use. Conductor sizing per code helps keep voltage drop within acceptable levels. Higher amperage increases the voltage drop. So the lesser amperage of the 240 volt unit will result in less voltage drop and greater efficiency. In this case, the difference will not be great, but it will exist.

It the AC rated 208-240 or one of these? Is the building 120/208 or 120/240? Do you have a lot of room in your service panel?

When specifying power-hungry, expensive laboratory equipment, I tend to stay away from stuff labeled 208/240 for a 120/208 building. The 120 option on 120 V outlets will do better with voltage reductions than 208/240 appliances powered by 208. The same may be true for AC compressors.

The 120 ac circuit will only require one space in your service panel while the 208/240 will require two. Balancing that, the cable for 208/240 will be less expensive because there is less copper in it. The latter is probably only significant if you have a large distance between the service panel and the AC.

You'll be better off with the 240v and I couldn't describe it any better than bus_driver did.

Is the 240 available within the reach of the electrical cord or will it have to be added?

"So the lesser amperage of the 240 volt unit will result in less voltage drop and greater efficiency."

Providing closer to nominal voltage under starting surges also shortens the start time and results in less equipment heating and wear and tear.

The 240 V unit is very likely to last longer for this reason.

While many people have made points here that are technically correct, the big picture is that you will have about the same installation and operating costs for both systems. Both use the same process to cool air and the amount of cooling is the dominant factor in determining operating costs. The only way you are going to save significant money is by raising the temp a degree or two. All the other considerations are just nibbling around the edges and are only going to amount to a few pennies per day.

If this is a portable aircon that you may take with you when you move, I'd suggest a 120v unit for its easier installation in most other homse and apartments.

If it's to become part of the structure, it makes almost no practical difference for a residential user. Choose on the basis of SEER (efficiency), noise level, serviceability, and reputation for durability, and let the installer worry about the voltage.

https://www.heating-air-conditioning.net/

120 0r 220 Air Conditioner.

BTU, or British Thermal Unit, is a thermal heat measurement. It takes one BTU to lower the temperature of 1 lb. of water in one minute. A 120-volt air conditioner typically has between 5,000 and 14,000 BTU, while a 220-volt air conditioner has 15,000 to 23,000 BTU. The BTU you need depends on the size of the room you want to cool. A very powerful 15,000 BTU air conditioning unit will not cool a 100-square-foot room better than a 5,000 BTU unit -- it will cool the room unevenly and run overly short cycles. If a 5,000 BTU air conditioner is placed in a 1,000 square foot room, it will struggle to keep it cool. Always measure the room you're cooling and use the size to determine the BTU needed.

Circuit Compatibility

A 120-volt air conditioner plugs into standard wall outlets, making them a convenient choice for most homes.

A 220-volt air conditioner requires a larger three-pronged outlet for heavy-duty appliances. If you have a very large space that requires more than 15,000 BTU to cool it, you'll need to have an electrician install a 220-volt outlet. It's not possible to force a 220-volt plug into a 120-volt outlet, and it's dangerous to try.

Efficiency

When running cycles that are equally long, a 120-volt air conditioner and a 220-volt air conditioner are equally efficient, using roughly the same amount of energy. Both types run inefficiently if improperly placed -- 120-volt air conditioners are inefficient and use excess energy when they are placed in a room that's too large for it, and 220-volt air conditioners lose efficiency when placed in small rooms. To ensure the maximum efficiency of your air conditioner, match the BTU to the room size.

Portability

Typically, 220-volt air conditioners are larger and heavier than 120-volt air conditioners. 220-volt air conditioners for home use are either window or portable floor units, while 120-volt are available in more compact versions as well as portable versions. If you plan to move the air conditioner from room to room, a 120-volt unit will run connected to any standard outlet and is light enough to move easily once drained.

Since the OP asked, Global Warming has caused the pendulum to swing in favor of two units... and the Op has moved to Cleveland.

"It takes one BTU to lower (sic) the temperature of 1 lb. of water in one minute."

So very close.

Many thanks to the user MiniSplit Heat, I was just looking for this information and you helped me a lot. I still decided to use an air conditioner that uses 220-volt. On the advice of a friend, I chose a Split system Panasonic CS-PA7GKD and I am very glad that I chose it. It's much better than my old AC that just spent my money on. Good that on https://www.socool.sg/ I was able to find the guys who installed it for me because I never did it myself and I was afraid to spoil something. As for electricity bills, they went up by about 50 $ in the summer.

One thing to keep in mind is that the 110 volt AC may have a higher EER, because manufacturers have an incentive to keep the current demand to a minimum, because many of their customers may not want or be able to run a special line. Also, there may be better sales on the 110 volt units.