The term "great leader" isn't really a meaningful one as there are many types of "greatness." Skilled military leaders, for example, at not be good at administration, whereas technocrats who are expert at policy or economics may not be charismatic figures. Popularity is necessary for getting votes in democracies, but not essential in other forms of government.
John Smith seems to have been a colorful character, but better at daring feats and adventures than at sustained accomplishments required for governing. He seems to have spent a fair amount of his life getting into and out of scrapes of various sorts, and seemed to work better independently than as a member of a team. He tended to act autocratically, rather than being skilled at motivating the colonists.
Although starvation and disease would have made the colonists unhappy no matter what, a leader who was better at inspiring them might have received fewer complaints.