The most noticeable difference between the Rimfire VR2, V2, and the V3 is the length of the ceramic outside of the engine. The longer VR2 was considered a racing plug back in the early days of ignition engines and due to the length of ceramic one could apply much more voltage to the plug before it would short, or jump to ground on the outside of the engine. That way they could run the plug much hotter and cleaner. Remember in those days they had no way of shielding the spark plug or preventing the spark from jumping to ground. Today we have rubber boots that can prevent this problem so we can apply much more voltage to a shorter plug and prevent spark jump.
Physically our V3 varies from the VR2 and V2 internally and externally. The thread length on the V3 is .050 shorter than the VR2 and V2, but it is engineered to perform the same; although minor variations in rpm can occur simply because of the direction of the ground electrode when the plug is installed. Something as simple as changing the gap on a plug can improve performance too. The VR2-L, which is a longer thread (deep reach) spark plug designed to run hotter than the VR2 for those cooler running Hit and Miss type engines.
The primary reason for the three styles today is esthetics - and you should choose the plug that looks the best in your engine. The most commonly used style since the 1940s has been the longer VR2 style. This is probably due to its reputation as a racing plug.