This is a tricky question, because the meanings of these terms have shifted, gradually and inconsistently, over the past century and a half.
In the early 19th century, both meant pretty much the same thing: "averse to social intercourse, uncompanionable". During the course of the century, however, unsocial came more and more to mean "hostile to society" and particularly "hostile to the existing social structure". By the end of the century which of these meanings was meant by any given use of unsocial was evident only in context. Bernard Shaw played on that ambiguity when he titled his last novel An Unsocial Socialist, for its hero is both.
Unsociable continued to have its original meaning, and still does today.
In the 20th century a third term came into play: antisocial. This had been around since the 18th century, but took off in the 1890s, in both BE and AE, as the favored term for designating both those who were politically opposed to the existing structure and those whose actions or opinions were regarded as dangerous to society at large. In the latter sense particularly it has taken hold in the social sciences, to such an extent that since about 1930 it has completely outstripped both unsocial and unsociable in frequency of use.
Today, at least in AE, unsocial has pretty much reverted to the older sense, and is used interchangeably with unsociable - see Bill Franke's answer.
I notice, however, that your screenname suggests you are a speaker of Indian English. Here the situation is somewhat different. A quick Google on "unsocial India" reveals a preponderance of hits where unsocial bears a meaning which in AE would more likely be expressed with antisocial.
I suspect, therefore, that your examiner wants you to select unsocial, suggesting one whose behaviour and attitude exhibits hostility towards other team members, excites hostility among them, rather than unsociable, suggesting merely one who does not participate much in team social activities.