Cloud didnt have any memories of Aerith from Zack. He took on Zack's SOLDIER first class rank, his dream of being a mercenary, and his place in the events in Nibelheim. That's all. He only got the 'memories' of Nibelheim because he was there, he simply interjected himself where Zack was.

That being said, I think Cloud would have reacted as he did if Sephiroth had killed anyone; Tifa, Barret, anyone. I dont think he did it out of love for Aerith (I dont think he loved her to begin with), he did it because he failed her and because Sephiroth took an important person away from him (again, would have been the same if it had been Tifa or anyone.)