PNEUMATIC TYRES are usually fitted to engine powered forklift trucks rather than electric powered machines. That said, there are some electric forklift trucks fitted with pneumatic tyres but they are quite rare. Should you choose one you may find it has a more powerful motor and bigger battery than it's cushion tyred counterpart so it can more closely simulate an engine powered truck.
Pneumatic tyres give a much better "ride" than solid cushion tyres and should be used where the floor surfaces are rough. The downside to them is that they can obviously be punctured. To get around this You can also get puncture proof pneumatic tyres at extra cost which have a steel band inside to protect them.
If you are thinking of buying a forklift truck powered by diesel of LP gas you will nearly always have the option of having pneumatic tyres and rough terrain trucks always have them fitted.
SUPERCUSHION or super-elastic tyres are a good compromise and they are often available for on both engine powered and electric powered forklift trucks. They have a similar profile to a pneumatic tyre but have a harder outer carcass and a softer rubber core giving some protection against bumps whilst remaining puncture proof. These tend to be quite expensive but last for a very long while.