Sorry if this question appears to be a bit random, but I was curious to read your learned opinion about which of these two unions is more feasible and has more potential.
Today Italy is an independent nation, but for large tracts of its history it has been the field of battles and intrigues between the Habsburgs (of Spain and later of Austria) and France. My question is, could there exist a Timeline where (most of) Italy is solidly controlled by France or Austria, possibly even to the present day (I know, nationalism makes this extremely difficult, but...)? The institutional asset could take many forms from a unitary state to a federation to a personal union to weirder arrangements.
Possible PODs are things like France doing much better in Italy during the War of Spanish Succession (my favourite would be Eugene of Savoy fighting alongside France) or Austria managing to retain Naples and Sicily during the XVIII century, in any case I would not focus too much on the POD, but more on the socio political viability of each union and on the possible economic and military effects.
I would say that a Franco-Italian union is more likely to function in the long term because culturally French and Italians are much coser than Italians and Germans, Hungarians, Bohemians etc. and the economies are similar (maybe too similar?). On the other hand the Habsburg have imo a better claim on Italy as part of the HRE (atleast the north) and the economies are rather complementary.
Militarily Italy has a great strategic position for controlling the Mediterranean, this would probably be a boon to France more than Austria, but likely not enough to turn the tides against the Royal Navy, because there wasn't any "blue navy" tradition in any Italian state in the XVIII century, apart a bit in Venice, but I don't think Venice could be annexed by France before the revolutionary wars equivalent, if it happens.
Resource wise Italy doesn't add much other than manpower (particularly useful for France if she undergoes the same demographic decline as IOTL) and maybe sicilian sulphur.
EDIT: in both cases I envision the fusion to be rather gradual, with statelets like Parma or Modena being gradually included by inheritance and/or war, while the Papal States would likely remain untouched for the foreseeable future unless something like the French Revolution happens. Obviously if a single power controls the rest of the peninsula it will have the strenght to heavily influence the Papal States, but annexation is out of the cards barring revolution I suppose.