When discussing premodern republics it is usually stressed that despite being "self governing" these were no means inherently democratic, governance was often highly closed off and social life still characterized by social stratification and hierarchy. Which leads to the question of what the experience of republics were for those who were shut out of a direct role in government as surely as if they were in a princely state. Did the republican systems of government in Florence provide real benefit to the poor as opposed to the despotism of Milan? Was it "better" to be poor in Venice than in Naples, or did these details of government structure not really effect those outside of the small group eligible for officeholding?
It's a bit of a chicken-or-egg question, isn't it? Even modern liberal political economy, which correlates inclusive institutions to better economic outcomes, doesn't really tell us which way 'round this happens (does prosperity lead to political inclusiveness, or does political inclusiveness lead to prosperity?).
Thing is, it's really difficult to derive numbers on things like medieval or early modern inequality, or how better or worse off poorer people might have been. While every city had its religious institutions providing relief for the poor, we can't really know which one was more effective. Information is also limited on things like wage or price data. In fact, economic historians alternatively assume that Tuscany, starting from the 13th century, was either representative of the whole of center-north Italy or the most prosperous part of center-north Italy. Both conflicting conclusions are derived from differing interpretations of the fact that Tuscany is pretty much the only region with reliable wage data in the 13th through 15th centuries. So the only thing we can say for certain is that in this early phase the "very republican" Tuscany produced a lot of paperwork. Is the presence of middle management (since time immemorial the main generators of paperwork) at the very least a testament to the presence of a large upper middle class? I guess, why not.
We get better price data starting in the 17th Century, when Lombardy also enters the chat as a source of reliable data. But the tragic thing for your answer is that by this time, both Lombardy and Tuscany have experienced republican regression and are now autocratic states. We can, if we absolutely have to, assume that even in this late era Tuscany's institutions were more inclusive, given it's longer history as a republic (and longer rule by an Italian dynasty) allowing republican institutions to leave a more lasting mark under the monarchial surface (although we can also argue against this - Milan, while alternatively under French, Spanish, and Austrian suzerainty, was generally governed by a clique of local grandees with little or no input from whatever monarch possessed the city) but still, no matter - even net of these differences in both cities the only real pressure on wages appears to be population: wages increase after plagues, and slowly decrease as population rises. Republican innovations (or regression) have little statistical impact. Macabre, isn't it?
Do you have doubts on how reliable this conclusion is? You should. Even our wage data, where we have it, is really limited. We have two main institutions providing us data in Florence and Milan: The Opera di Santa Maria del Fiore in Florence and the Veneranda Fabbrica del Duomo in Milan, charged with the maintenance of their respective cathedrals. This means that we are using stonemasons and other construction workers as stand-ins for the entire economy, ignoring that for whatever reason they might be insulated (or particularly affected by) exogenous shocks on wages. And do we have similar data for, say, Venice? Not really - Venice's cathedral (which is San Zanipolo, and not St. Mark's, for starters) is mostly decorated with small-scale private chapels and did not require the sort of continuous maintenance that Santa Maria del Fiore required, nor did it experience near-continuous construction and constant design changes like the Duomo of Milan. So no, we don't have equivalent data for Venice. Blame it on the Venetians being merchants and entrepreneurs, more interested in one-off payouts following mercantile expeditions rather than diligent florentines or milanese recording their worker's wages. I don't know.
We do have qualitative evidence on the presence of destitute poverty in Rome in the 16th and 17th centuries. The initial cause seems to have been the sack and occupation of 1527 - the Italian wars had themselves started a small trend of pushing rich and poor Italians alike away from the north and towards the relative safety of Rome, especially for people in professions which were "naturally itinerant" like entertainers or mystics (but also artists and philosophers) so this this last city's sack was a definitive blow to people who had nowhere else to go. However, you can imagine the population of aristocrats relocating to Rome, as well as itinerant clerics and other vagabonds, represent more of an anecdotal social phenomenon rather than a statistically significant one. If anything, the pervasive commentary we have on the presence of poor mendicants in the city of Rome might tell us that the presence of religious institutions are not a guarantee of strong institutions providing welfare, and that's predictable enough: before anything is redistributed, there needs to be something to be redistributed in the first place, and Rome was never particularly economically vibrant after the end of it's eponymous empire (in fact, Rome only begins figuring among Italy's largest cities after the country's unification).
Anyway, that's my not-entirely satisfying answer. Were more inclusive republics more prosperous or less unequal? Probably, but who knows. We're still waiting to discover a 15th-century venetian salary book.