I have read about 2/3 of the Qu'ran in English and all the Bible. You? I can see the main/most important distinction is this:
The Christian is 100% sure of salvation if they've trusted in the death and resurrection of Christ--what Christ suffered on the cross--and the Muslim has to be very religious to hope to maybe get to Heaven. Both of those positions cannot be correct.
What did Jesus pbuh say in this regard?
Mark 10:
17 And as he was setting out on his journey, a man ran up and knelt before him, and asked him, “Good Teacher, what must I do to inherit eternal life?” 18 And Jesus said to him, “Why do you call me good? No one is good but God alone. 19 You know the commandments: ‘Do not kill, Do not commit adultery, Do not steal, Do not bear false witness, Do not defraud, Honor your father and mother.’” 20 And he said to him, “Teacher, all these I have observed from my youth.” 21 And Jesus looking upon him loved him, and said to him, “You lack one thing; go, sell what you have, and give to the poor, and you will have treasure in heaven; and come, follow me.” 22 At that saying his countenance fell, and he went away sorrowful; for he had great possessions.
23 And Jesus looked around and said to his disciples, “How hard it will be for those who have riches to enter the kingdom of God!” 24 And the disciples were amazed at his words. But Jesus said to them again, “Children, how hard it is to enter the kingdom of God! 25 It is easier for a camel to go through the eye of a needle than for a rich man to enter the kingdom of God.” 26 And they were exceedingly astonished, and said to him, “Then who can be saved?” 27 Jesus looked at them and said, “With men it is impossible, but not with God; for all things are possible with God.”
Here we can see you have to put in the effort, to strive and struggle, to follow the commandments and ultimately rely upon the mercy of GOD to obtain salvation.
This is hammered home in the later Gospel of Matthew
Matthew 5:
17 “Think not that I have come to abolish the law and the prophets; I have come not to abolish them but to fulfil them. 18 For truly, I say to you, till heaven and earth pass away, not an iota, not a dot, will pass from the law until all is accomplished. 19 Whoever then relaxes one of the least of these commandments and teaches men so, shall be called least in the kingdom of heaven; but he who does them and teaches them shall be called great in the kingdom of heaven. 20 For I tell you, unless your righteousness exceeds that of the scribes and Pharisees, you will never enter the kingdom of heaven.
Not so different to what is taught in the Qur'an.