score:9
Both Turin and Genova are two big cities able to provide you a lot of attractions, the choice of the best one really depends on what you are interested in and what kind of cities you prefer in general.
As a personal point of view I consider Turin far more elegant than Genova: nice streets with elegant buildings, the possibility to climb (by car or by a little old train) on the hill of Superga close to the city and have a wonderful view on the city and the Alps in the background, a lot of history related mostly with the period of the wars that brought to the formation of Italy as a single state (but also big roman ruins), the biggest egyptian museum in the world outside Egypt and a vibrant night-life.
Genova has a strong connection with the sea: the wonderful acquarium is considered its main attraction and its internal streets (Carrugi) are quite peculiar too. Even Genova has a rich history and has been one of the major european cities in term of power, so you can find several nice buildings reflecting this. I don't know about the night-life there but I never heard anybody praising it like I did with the Turin one.
Regarding the food, both have particular regional dishes (pesto from Genova for example) but I guess that Turin with the wonderful wines from Piemonte and the "fassona" meat could be considered better even from this point of view.