What are the differences in performance for IPv4 and IPv6? Is there much of a difference in speed? and what are some of the methods that could be used to test this?
Based on real-world Internet measurements by large companies, IPv6 has a slight edge in performance. This may be due to several reasons, such as the simplified packet header, or it may be due to other factors which have nothing to do with the protocol itself, such as more lightly loaded DNS servers.
As far as testing it yourself, it would be the same way you test anything else. Set up whatever applications you want to test, use each with each protocol, and perform measurements. There are far too many different applications which use both protocols to give you detailed tests, and each person has different ideas about what results to observe, and what they mean.