I would take the 240V one. The generator won't need to produce as many amps to run the 240V one leaving more margin for your other stuff. Always try to run the big motors and compressors at 240V if possible. I'd pick the smallest 240V items I could find (e.g. a 10A 240V unit over a 15A 120V unit). If the power draw or cooling capacity was equal, the 240V unit would draw half the amps of the 120V one. In your examples, the 240V AC is larger, but not twice as large. So it should draw less amps than the 120V unit. I'd look at amp nameplates on what you buy to compare the load.
Remember that your generator is really a 240V model and has two separate legs that can generate about 25 amps. If you load down one leg with a 15A air conditioner, you need to manually balance everything else and put most of it on the other leg. A 240V 10A generator will take 10A from both legs leaving 15A on each (and the startup surge will be shorter and smaller on the 240V unit). You should then try to spread the other loads across both generator legs.
With any AC unit on a generator, you need to understand which plugs go to which leg, and having power or amp meters on each leg would be a real plus to keep it more evenly loaded. Also, look into the surge rating of your generator. Some may not have the ability to start an airconditioner because the locked rotor startup amps are huge (50 to 100 amps). If the generator can produce for the quick startup time, the AC unit may not start at all. Ideally, the AC unit would have a nameplate amp rating of no more than half the amp capability of the generator.