I don't really know much about the man's character, but one change would be that the ruling coalition might become a tad less monolithic, having a leader come from the SACP rather than the ANC proper itself. How that would change things generally I don't know.
Assuming all else goes roughly similar I would suspect Hani wouldn't have pulled a Mbeki re HIV/AIDS. Re Zimbabwe, well, I guess this depends on why you think SA holds the position it does.
Regarding your first comment, Hani's membership of the SACP would have made no difference. Practically every senior member of the ANC then (and now) was, or is a member of the Communist Party, and the two are still in an alliance, with the biggest trade union federation, Cosatu. Despite the SACP's influence in the ANC, the policies followed post-1994 could have come straight out of
Neo-Liberalism for Dummies.
However, Hani was definitely more of a man of a people, and Mbeki would have faced a massive scrap with Hani to become Deputy President of the ANC. There is a conspiracy theory that Mbeki was in some way involved in the murder.
With Aids and so on, I don't know if Hani would have followed the Mbeki doctrine. He seemed independent minded, and not as race conscious as Mbeki, so I think things may have been different if Hani had lived. Perhaps we would have had a Hani presidency from 1999-2009, with a more orderly transition than we are having now. A Hani Presidency may also butterfly away Zuma Deputy Presidency, and may have an impact on how the arms deal plays out.