Short answer is that we reject both.
The concept of fallen angels does not exist in Islamic theology. We believe that Satan was cast out of Heaven for refusing to bow to Adam, but the Qur'an identifies Satan as a jinn-- not as an angel. A jinn is a type of creature that Allah created from fire. Though they are invisible to us most of the time, they, like us, are commanded to believe in Allah and obey His commands. Just as there are good humans and bad humans, there are good jinns and bad jinns (Satan is obviously of the evil variety). "Behold! We said to the angels, 'Bow down to Adam': They bowed down except Iblis. He was one of the Jinns.." (surah 18:50). This story is narrated all throughout the Qur'an. Iblis lived among the angels, in Jannah [Paradise], but he chose to live with pride.
As I said, we don't believe in a race called the Nephilim, but we do believe in a nation of giants. They were from a nation called Ad and their prophet was a named Hud [peace be upon him]. They were descendants of prophet Noah and they were from Arabia. "To the 'Ad people, (We sent) Hud, one of their (own) brethren: He said: 'O my people! worship Allah! ye have no other god but Him will ye not fear (Allah)?'...'Do ye wonder that there hath come to you a message from your Lord through a man of your own people, to warn you? call in remembrance that He made you inheritors after the people of Noah, and gave you a stature tall among the nations. Call in remembrance the benefits (ye have received) from Allah: that so ye may prosper'." (surah 7:65,69)
They were not only huge, but they were also blessed with numerous fancy buildings and temples [26:128-29], a lot of physical strength [26:130], cattle and a big population [26:133], gardens and springs [26:134], high intelligence and skill [29:38]. Most of them rejected Hud's message, so God destroyed the disbelievers of Ad with a wind storm (possibly a tornado).