I think the obvious point of comparison between these two great texts is the way in which both present Africa as being profoundly impacted in a negative form by colonialism. In Heart of Darkness, it is clear that again and again the only legacy that the white's colonialism of Africa has brought is death, decay and exploitation. Perhaps one of the most chilling examples of this is seen in the "grove of death," where the blacks who are presented to us are clearly dehumanised and have become nothing more than objects:
"Near the same tree two more bundles of acute angles sat with their legs drawn up. One, with his chin propped on his knees, stared at nothing, in an intolerable and appalling manner: his brother phantom rested its forehead, as if overcome with a great wearines; and all about others were scattered in every pose of contorted collapse, as in some picture of a massacre or a pestilence."
Clearly the tragedy that Marlow sees in this grove of death is a comment on imperialism and colonialism which has only brought difficulties to Africa.
Likewise, in the same way, Things Fall Apart spends many chapters introducing us to an African culture that is shown to exist perfectly well by itself. However, it is the arrival of the white missionaries which herald problems for this culture, and divide it and begin to destroy it. Africa yet again is presented as only being impacted negatively through Western involvement in its affairs and business.
This I think is the most obvious parallel. You might like to think as well about the specific way in which Africans are presented in both novels after the impact of the whites, and how, even with laudable intentions, the overall impact of colonialism is shown to be profoundly negative.