It's difficult to discuss one type tire without comparing it to other types available.
Air tires give a softer ride, a larger "foot print" for better traction and floation. Air tires are also easier damaged and subject to punctures & flats. A variation to the air tire is "foam filled". It has a little firmer ride a little less "foot print" as compared to a true air tire. It is also somewhat of a skill to get just the right amount of foam in the tire. Too little and the side walls flex too much and heat and and are subject to side wall damage. Capacity problems can result from tires with too much give as well. Too much foam and the tire rides too firm and wears out the center of the tread.
Solid pneumatic tires have a smaller "foot print" and generally have less traction in gravel or soft surfaces. They also ride the firmest which can lead to product damage as well as being somewhat hard on the equipment. However, they are much more difficult to damage. From my point of view Tire life should be secondary. There is not a "best" type tire without considering the application. There are pros and cons to each type tire. I have not attempted to discuss tire cost as tires should be chosen for the application and not just because they may be cheap.
It all depends on which traits best serve the needs of your application as to which tire you should choose.