Hello Simon -- Interesting question. As a general rule I would say ~3 inches is the delineation between the two when considering the Dai - Sho. However, having said that it's not so easy. To understand the tsuba you have to understand the evolution of the sword along with how it was used and worn. First, the tsuba was basically used to keep the hand from being forced onto the blade in use, therefore the size is not all that relevant for this parameter. Second and more importantly for our discussion, it must act as a counterbalance for the blade in hand to allow function. This will vary by type of use; a tachi being used from horseback will have different requirements than a katana used with two hands at ground level as opposed to an earlier uchigatana used in single hand technique by a foot soldier. If you visualize a Kamakura Jidai tachi well over thirty inches in length you will see the need for a larger and heavier tsuba to counterbalance the blade in hand (and also slung for that matter as otherwise it would tend to fall vertical to the rider). A shorter more slender Muromachi Jidai uchigatana used in single hand technique would require a smaller lighter tsuba (think Kanayama). An Edo Jidai Shinto/Shin Shinto Katana would require a larger and often heavier (thicker) tsuba to balance a longer and heavier sword. Material used will also affect size. And on and on. A good read is 'Tosogu no Kigan' by Sasano which although in Japanese has English explainations to the pictures and offers quite a bit of information on his theories on this subject. Some will argue he was a bit too radical in his age estimates but the overview of knowledge is good. All of this also helps to explain why tanto and koshigatana often had Aikuchi type koshirae without tsuba along with the way they were worn being thrust into the waist (koshi) band as a tsuba would tend to be uncomfortable in this position.
PS: I hope this helps to answer the question as to why we study this field also -- it's just very intersting history too!