The two classification models SLATES and FLATNESSES, both highlight what each type of enterprise 2.0 software is classified by, and what it does. I agree with Dion Hinchcliffe, heres his blog here with a bit more detail than the text-book http://www.zdnet.com/blog/hinchcliffe/the-state-of-enterprise-20/143. Now with me agreeing with which is better the third as coined in Niall book simply classifies them by the 4C’s, which to me personally is easier by far to understand and is more easier to group and compare with the actual software that has been classified.
The formality/interaction graph is followed to show how a company may implement the different types of social media, as mentioned by Niall Cook(2008) Enterprise 2.0: how social software will change the future of work.
My Social networking Journal 