There are many religions but all of them have some similarities, the basics of religions about God, love, faith, ethics, sin, after-death...Most religions consider the first duty of their members to recognize this Supreme Being, to adore Him, to praise and give thanks to Him.
So, I guess you are picking your similarities and differences from only two
specific religions, no?
What for the Golden Rule? Yes, most religions preach and try to practice the Golden rule, love each other, because we all are brothers in God. So, I guess that is another similarity, not just in your Muslim or a Christian's Chrstianity.
Most religions agree to preach and promote good ethics, good human conduct in the light of good moral principles. So, I guess this is another similarity that you overlooked in order to benfit your thread topic.
So, in reality, there is no Islam vs Christianity. If there was, then the same would be for Islam vs Judaism, or Islam vs Buddhism, and so forth..
Thankyou for your listening Islam person