Florence Tourist Board has been collecting data about admittance tickets to museums for years now. You can download here a pdf table where museums are listed according to the body they are managed by: state-run museums, city council museums and museums run by other bodies.

If you go through the figures you will see that State-run museums (also called Polo Museale Fiorentino) can boast a positive variation of +6,11%, while museums run by the City Council did still better, with an increase of 40,55%. Of course the main attraction is still the Galleria degli Uffizi, followed by the Galleria dell'Accademia and Pitti Palace complex.
Palazzo Vecchio, the seat of the Town council, has been rightly rewarded for its nightly openings and initiatives, considering its increase of 49,57% compared to the previous year. The novelty of 2010 was certainly the new Galileo museum, already known to the public with the name of Istituto e museo di storia della Scienza. The visits in the 2010 increased of 86,67 in percentage.