Most suitable biodiversity index
It sounds like you are interested in beta diversity which is the change in taxa composition (i.e., alpha diversity) between plots.  There are a number of approaches to calculating beta diversity and the correct choice generally depends on the question(s) you are trying to answer.  The most common approaches are very well described in this paper: 

Anderson, M. J. et al. 2011. Navigating the multiple meanings of Beta diversity: a roadmap for the practicing ecologist. Ecology Letters 14:19-28

P.S. I am not familiar with Disney's index so I cannot comment on its merits.

P.P.S. You may also be interested in this question.