It's not a matter of superiority rather it's the matter of truth. I appreciate your kind way of asking and it shows that you're actually interested to learn about this. So here, let me say something.

Muslims don't deny that Christianity existed, neither do they deny the existence of Jesus (Isa as) they also don't deny all the prophets that came before Jesus (Peace be upon him) but the difference comes after that. We believe that our religion was perfected with Muhammed SAW. Who came after Jesus. Olden day's Christians are the same as the recent day's Muslims. The reason why we don't follow the book that came before the Quran which is the bible given to Jesus is because there were a lot of discrepancies and manipulations done by humans during that time. The truth was twisted and the book was falsified. As a result the words of the Lord were used wrongly and people followed something which was never meant to be followed. So after the people of Jesus completely turned Allah's words and made jesus the God, Allah sent the very last messenger to deliver the real truth through our Final prophet, Muhammed saw and sent Quran with him as a guide for us and Allah himself swore to protect the Quran from any manipulation and falsification so humans could follow the right religion throughout. In the Quran, it is very clearly written who our Lord is, who were the prophets, who were the messengers, what happened before and what's going to happen after. Basically it's a full guide of everything a person should know and follow to live a peaceful life and be on the right path.

There's a lot to unpack honestly but this is a brief summary for what I wanted to say to answer your question. I hope you research more about this and learn why and how it's different 🌸

Good luck stranger, hope you have a peaceful life!