sociality 1a. The state or quality of being sociable; sociability. 1b. An instance of sociableness. 2. The tendency to form communities and societies.
sociability 1. The disposition or quality of being sociable. 2. An instance of being sociable.
Their meanings should derive from the adjectives 'social' and 'sociable'. The less complex, sociable, means to be fond of the company of others, or to be pleasant and friendly. It can also mean "affording occasion for agreeable conversation and conviviality." All in all, it conjures up the image of agreeable interaction. 'Social', on the other hand, is a more far-reaching term. A person is social by simply being present in a group, or attending a get-together, but he's not necessarily sociable.
In the following COCA extracts, the terms appear synonymous:
The organization of a memorable and peaceful festival was a triumph for the committee and for the town as a whole, since festival periods are noted as occasions during which alcohol and intense sociality set a backdrop not only for pleasant celebration but also for friction and violence between men.
Standing in the center of the room, Captain Halvorsen is a tall man with thinning red hair; he smiles politely as he talks to the passengers. Maud guesses that he must dread this evening and the enforced sociability.
However, in the next passage 'sociality' could hardly be replaced by 'sociability':
The sociality of some groups is short-lived: in some spider groups the siblings remain together for a couple of instars after eating their mother, and young scorpions remain with their mother [for] part of their development.
From the BNC and COCA search results of 'sociality' and 'sociability', it can be deduced that, of the two terms, 'sociability' is the one you'd want in your everyday vocabulary since 'sociality' is highly academic: 95% of its results derive from academic sources, 5% from magazines, and practically none from fiction, newspapers or spoken language.