Am reading John Kelly's The Great Mortality about the plague, which is repeating a characterization I've heard elsewhere: that cities like Genoa, Venice and Florence were exceptionally wealthy, sophisticated, stylish - and generally advanced, it seems. Were they in fact categorically different from other European cities at the time?
Absolutely. Throughout the post-roman world, Italy continued to be the focal point of the Mediterranean (and Western European) economy until it was overtaken by atlantic trade.
Italian cities and the states centered around them were small and consequentially well-balanced, fostering intense military, economic, and cultural competition. Nearly all of these cities had a legal system based on Roman-era freedoms and enfranchisement, with impersonal codified justice and protection of property rights, not just land rights. This was all capped off by the Mediterranean trade, which created extensive networks exchanging goods and services operated by a large middle class, which wasn't willing to be taxed without a say in the matter, creating inclusive institutions.
The Mediterranean is a basin that is particularly favorable to the formation of cities; there are numerous seafaring trade routes and high agricultural fertility levels which can support populations that aren't farming. These things really do culminate in Italy; it's easy to see why in the urbanized Roman heartland of north/central Italy citizens would preserve rights and freedoms. These institutionalized rights and freedoms included the representation of the merchant/artisanal upper class in civic government, leading to a legal system favorable to economic development and fostering a relatively mobile society (the lines between a low-level member of the landed nobility and high-level merchant are indistinguishable in Italy by the eleventh century).
Other politically fragmented and heavily urbanized areas, like the Netherlands, developed a similar set of laws and institutions. In fact, the Netherlands come in a close second to Italy in economic development indices through the middle ages up until the early modern era, when the double whammy of the Italian Wars and the boom in atlantic trade sent the Netherlands on an unparalleled growth trajectory while the Italian states went into protracted stagnation.
The largest data set on economic development from the fall of the Roman Empire to the modern day was published in 1990 by the British Economist Angus Maddison (updated by Bolt and Van Zanden in 2013) which pretty much shows how Italy really was well ahead of the rest of Western Europe up until the mid sixteenth century.