Is it worth it to wait and attend free museum Sunday in Florence or are the crowds overwhelming and better to go another day?
It probably matters which museums you're interested in.
Agree, it depends on which museums. Uffizi is a multiple hour wait all day long, but you can sometimes get into the Accademia late in the day without too long a wait. Medici Chapel lines are long most of the day. Pitti Palace/Boboli Gardens lines look long but move quickly as the complex is so large. Bargello usually isn't too bad a wait. San Marco Museum is often closed on the free Sunday. Also remember that it's only the state-owned museums that are free, so there's no free entry to sights such as the Duomo Museum and Santa Croce church. The TI offices may have a list of the state-owned museums and their hours.
It's not worth the savings in my opinion. Follow your heart not your wallet. We went to a less popular museum in Rome and it was unpleasantly crowded due to the free admission. To add to the fuzziness, there was a government proposal in the news to end the free Sunday so who knows what the future holds.
I am visiting in October on the first Sunday and decided to make reservations at the Uffizi and Accadamia the day before. I didn't want to miss the chance at seeing them or spend my limited time waiting in a line. I made a reservation for the Duomo climb for Sunday as it is a reservation process anyway. I'm only in Florence two nights so it just made more sense for me. I had budgeted for the tickets anyway, but I took advice from this forum and from a guide in Florence, who I will be meeting with for a walking tour. Your experience with it may vary depending on whether you have the time to save some Euros. If you decide to wait and do the free day, I'd be curious to hear how it turns out. I'll see the lines myself, but I'd like to know just how long the wait really ends up being for the sites I mentioned. Good Luck!
Jeff