My feelings about this game should be obvious. It has very little direct player interaction. I seem to always lose 5 player games of it. It is full of calculations (too do well, it feels like you need to do lots of arithmetic in your head). It is part of the same Alea line that produced Puerto Rico.
But I like this game a lot.
What is it about 7 auctions and 14 actions that means 90 minutes of fun? I think part of the enjoyment is maximizing limited resources (in money, actions, and so on). The punishment (in lost VP) for over estimating or under estimating your money needs forces you to plan ahead. The unpredictable result of auctions frequently breaks plans and you need to construct alternative plans.
There is limited player interaction on the surface, but underneath there is a ton. Stealing artists and scholars from other players, the competition of auction, competition for scarce resources (like profession cards and freedoms), and so on.
Seating order does matter, but I don't feel there's seat binding, as in games like Puerto Rico. Due to the limited resources there is a chance that people in "bad seats" will have less chances for more profession cards, freedoms, and so on. Also the odd nature of the auction (must start at 200 and you must either increase by 100 or pass) means that some seats can be disadvantaged (value of a good could increase 500 florin by the time you get to bid on it again).
It is also one of the few games I've played that has any modeling of inflationary factors: each turn the minimum threshold for a work increases. There is also a great incentive to hold on to works without playing them for as long as possible (each turn you can get stuff to increase the work value).
Balancing this increasing value is a 3 victory point advantage given to the player who completes the best work (which is equivalent to an increase by 6 in its work value). This does give people sitting last more information (they can calculate if they will have the best work of a round).
Money seems tight. There are only 2 ways to get money in the game and both involve giving up points for florins. When you play a work you can take the work value in points or cash (200 florin to 1 point). If you don't think ahead, then you can convert points back into cash (1 point to 100 florin).
The only luck in the game comes from decks of cards, but you draw more than you can keep which allows skill to mitigate the luck of the draw. There is also a side game of placing your buildings and landscapes on your board. Each one is a weird Blockus-like shape. Once placed you can't reposition it. Also builders can change the rules for building placement (adjacent buildings aren't allowed until you have 2 builders).
Tough decisions. Long term planning. Never enough time to do everything you want to. These are the elements that keep me coming back to Princes of Florence. It is also a very different game depending on number of players (officially it plays 3-5, but , Wolfgang Kramer has written a 2 player variant that works surprisingly well).