For the full bore ball valve, the bore diameter ,the hole in the ball has the same internal diameter as the pipe, whereas the reduced bore ball valve has a smaller bore diameter than the internal diameter of the pipework it is on.For example, the bore size in a 4 inch full-port ball valve is 4 inch in internal bore, while the bore diameter in a reduced ball valve is 3 inch in internal diameter,or you could also understand like this, full bore through the port,  for example,4 inch full bore ball valve is 4 inch opening for the water flow.  

Full bore ball valve isused where their low flow resistance is of value such as on pump suction pipes, where a pressure drop can affect pump performance. They are also used in flows containing mixed liquids and solids where flow restrictions can cause separations in the materials causing buildups and thus reducing the flow in the pipes. Ruduced bore ball valve is used where pressure drop, turbulence in the flow and material characteristics are not a concern. They also have the advantages of smaller size and lower cost.

If there is no strict demand on flow rate,you could select reduced bore ball valve as the price is more economic and the weight is relatively a little lower.