Joseph, the son of Jacob, is an important figure in both Judeo-Christian and Islamic tradition. Sold into slavery by his brothers, who were jealous of his prophetic abilities and Jacob's favor, Joseph rose to become the king of Egypt, helped neighboring nations through a severe famine, and ensured the position of his lineage in the area before his death.
The main difference in the Koran's version is the detail; while the Old Testament's account is straightforward and short (of necessity, since it directly leads into the Exodus), the Koran's later accounting contains many more details in the primary text. Much of the inner detail in the Old Testament's version is told through commentaries written later. Joseph is considered a great prophet and forefather in Islamic tradition.
Of course, the other great difference is that while the Old Testament's Joseph attributed his fortunes to the Hebrew faith and God, the Koran's Joseph (naturally) attributes his fortunes to the Islamic faith and Allah; the idea is that even in Biblical times, before Mohammad, men of faith already recognized Islamic principles as true -- this echoes the Old Testament's adoption of Judaic principles long before Sinai.