A key verse as to why I don't believe Muslims and Christians serve the same God.

 

John 5:18-23(NKJV)

Therefore the Jews sought all the more to kill Him, because He not only broke the Sabbath, but also said that God was His Father, making Himself equal with God. 

Then Jesus answered and said to them, “Most assuredly, I say to you, the Son can do nothing of Himself, but what He sees the Father do; for whatever He does, the Son also does in like manner. 

For the Father loves the Son, and shows Him all things that He Himself does; and He will show Him greater works than these, that you may marvel. 

For as the Father raises the dead and gives life to them, even so the Son gives life to whom He will. 

For the Father judges no one, but has committed all judgment to the Son, 

that all should honor the Son just as they honor the Father. He who does not honor the Son does not honor the Father who sent Him.

Muslims do not honor Jesus as the Son of God.  They believe Jesus was a prophet but nothing more.  Not only that but they believe Muhammad was a greater prophet than Jesus.  The Scripture above seems pretty plain to me.