Each AMC will have their own funds, among different funds you have to select particular scheme which matches in all the selected AMC.
Ex: Tax advantage fund: all the AMC will be having Tax benefit fund or particular sector fund or Gold fund, Debt fund.
You can get the scheme details in the AMC scheme document.
Collect NAV data for the particular period and start applying any statistical tools to analyse. Sharpe, Treynors, Jenson model are models used in analysis of MF.
I think it will depend on the purpose of the research to be undertaken. On the basis of that,a few MFs may be selected and then the schemes of these MFs may be studied which are almost similar.Which field we want to emphasize will have to be decided first of all,it may be equity,debt or liquidity aspect.