Are there any differences in large or small pieces of root ginger?
Quite the opposite, large ginger rhizomes are more potent both in flavour and aroma, because those compounds take time in the ground to develop and accumulate... 

There's a Chinese proverb: "It's the older ginger that's got the punch /heat", referring to wisdom of the elders / the experienced...

The younger rhizomes have a milder flavour, and a smoother texture (the older ones are more fibrous) so are used for pickling in both Chinese and Japanese cuisines...