steen425: I agree with NFLwidow: that Venice is a great and romantic city, especially if you are planning to go in the winter. I love Venice in the winter (I was there both in summer and winter 2015 and while there’s really no such thing as a bad visit to Venice, the visit in the winter was a lot more fun).
Since tourism is so dominant in Venice and the centro storico of Florence, it’s rare for a restaurant to exist (or, in Venice, possibly even to survive) without tourist traffic. Now this does not mean that there aren’t very fine restaurants in both cities, but it does mean that the restaurants tend to be more expensive and you won’t be able to get that sense that you’ve “discovered” a secret little gem, which is really important to some people. But, if you just want good food, both cities will have you covered, for a price. The best restaurants in Venice really do, for obvious reasons, lean very heavily toward seafood and some of the most well-regarded restaurants in the city don’t have (or almost never have) non-seafood secondi. Florence is a meat city–cinghiale (boar) and the famous bistecca alla fiorentina are both common (cinghiale more in ragù for pasta), though you’ll also see rabbit and lamb, and there will be chicken and seafood/shellfish dishes at most places as well. In both cities you can do a nice small lunch for 10-20 euros/person. Most of my favorite spots for dinner in Venice start from 60-75 euros/person (I usually get either an antipasto or a primo, a secondo, wine for dinner, a dessert, dessert wine, and coffee), and the prices at my favorite places in Florence start a little cheaper.
ETA: In general, I would guess that most foodies would express a preference for Florence because if you are in Florence you have close access to other Tuscan or Umbrian towns, wineries and farms in the Tuscan/Umbrian countryside, and even fairly easy access to Emilia-Romagna, which is usually considered the great culinary region of Italy. Venice’s restaurants have a reputation for being mediocre and overpriced, which I think is unfair (a lot of them are, but not all of them). IMO, you just have to be more careful with your choices. But, then again, I just really like traditional Venetian cuisine.
If your foodie style is “I want gritty, super-local, authentic, uber-traditional, working people’s food and I want just about everyone else in the restaurant to be speaking the local language” you might want to consider Liguria. While Liguria is home to places that are overrun by tourism, like the Cinque Terre and Portofino, there are a lot of other towns on the so-called Italian Riviera, as well as Genoa (Genova in Italian), the region’s capital, where you will find plenty of places that come much closer to capturing that vibe (though, of course, no place is going to be 100% devoid of tourists). Ligurian cuisine is also kind of awesome, especially in winter, when hearty focaccia (in some towns focaccia col formaggio is a specialty), farinata, and traditional rustic dishes like rabbit, baccalà, and stockfish stew really hit the spot. You can also explore the Genoese fascination with American hamburgers (there are like three or four places in the city that draw pretty big crowds for their burgers). Prices in the best restaurants in the area won’t be cheap, but they won’t usually be as expensive as Florence and Venice. The best meal I had in 2014 was in a restaurant in Genoa. (FWIW, my best dish of 2015 was a fish soup that I had in Venice–I’m still not sure what my best overall meal from last year was.)