I've looked this up before. Some sources claim it comes out just as bad (or worse!) to use cloth, but when I looked into it further they were considering hot water washes and drying in a dryer. Whereas in reality you can usually cold or warm wash cloth nappies and line dry them. They also seem to consider them being used on only one child, when they can usually be reused for more than one child.

Looks like Wikipedia actually has a decent section on it: https://en.wikipedia.org/wiki/Diaper#Debate