see these links for Islamic point of view of the "sacrifice" matter.
http://www.islamic-awareness.org/Quran/Contrad/MusTrad/sacrifice.html
http://www.islam101.com/religions/christianity/sacrifice.htm
Islam/Quran doesnt make any difference among both of them. Whatever Abraham did with Hagar & Ishmael , according to Islam it was all a test for him from God , & not out of jelousy . God tested him with his prisest possession , his only son that he got after 86 years . In reward , he is the only one ( according to my knowledge ) whom God salutes (37:109) . He made him an honoured person , more than half of the world honour him & consider him their spiritual father .
The difference mainly comes from the Bible. Ishmael was not considered "in jewish circle" bc the word & concept
jew starts from judah s/o jacob s/o Issac(Israel) . At that time , jew was more of a race than a religion . There was no point of Ishmael being a part of a race that started centuries after him . So for jews , he was always an uncle , not a father . An uncle without convent , without a lineage of prophets . The world was soon divided into Jew & Gentile . Ishmaelities were among the gentiles , second grade humans .
The rift mainly comes from the fact that jews were waiting for Messiah , he came to them in the form of Jesus , the last promised prophet for israelites. Some people obeyed him , others didnt . People who followed him were called Christians , their theology
evolved , & later on Jesus became the son of God .
Jews didnt accept Muhammad b/c they thought that the last prophet/messiah had to come from jewish lineage ( b/c of the convent ) . Christians didnt accept him becaause Islam criticised the concept of "only begotten son" . This is the main rift. To muslims & christians , the messaih is Jesus , who came , & will come back again . To jews , he is still an unknown person .