Some people have inner ear problems and prefer slower inflation times so buying the best compressor is not necessary. The inflation time should not exceed the speed that a person can equalize their inner ears as the pressure increases. Just like you wouldn't speed to the top when scuba diving, they tell you to go very slowly so you don't damage your ears.
Note: Before you get a chamber know the inflation time. Some can take twice as long as another and some have flow rate setting where you can change the speed of air going into the chamber. If someone is putting a kid in it, I would make sure you know the correct flow rate so you don't hurt the ears.
Pressure in the inner ear if the chamber is inflated too fast can cause damage, not just the uncomfortable feeling. If the chamber inflates too fast with the factory compressor, you can always but a cheaper, slower filling after market compressor.
Some compressors have pumps that have have dual pumps so they can make the inflation time quicker. Many clinics use this because taking a few extra minutes over the day can mean an extra half hour they can charge someone to use the chamber. It is not fair to leave a someone in their and not know if the inflation pressure speed is too high. If the clinics has like 4 hyperbaric chambers, and they are putting one person in after another, make sure you request the technician to stay there and monitor yourself and especially a kid that doesn't know to ask to turn it down.
But, the good thing about the models with dual pumps is that once they inflate the chamber, they pump more air through the hyperbaric chamber and the air doesn't get as hot as their is more air exchange. Remember that moving air under pressure creates friction, this is how it gets hot. Even if a person is not in the chamber, the air will always start to get warm towards the end of the session.
Some compressors create more friction from the start depending on if its a piston or rotary or the other types of compression technologies. All of them will inflate the hyperbaric chamber but all do it with different speeds and frictions. If the person gets hot easily, you may want one type over another. Each hyperbaric chamber company usually has a different brand of compressor and inflation time. We timed each and each can be off by up to 3 times the speed.
Please see my air compressor page to learn more about the compressor to get a better understanding of the compressor before buying a chamber. See the air compressor page here.