I love both names, but I have a slight preference for
Florence. Its meaning is beautiful, it shares its name with a gorgeous city in Italy, and
Florence Nightingale isn't a bad namesake at all. I like that it has a bit of age to it. I find a lot of feminine names are cutesy, dainty, and darling.
Florence has strength. She's not there just to look pretty. She's admired because of her intelligence and work ethic.