Muslims believe that Jesus and Muhammad were both prophets and messengers of Allah. Peace be upon both of them. Muslims will not belittle any of God's prophets or reject their message. The Qur'an tells us to declare our faith in all of the prophets including Abraham, Moses, and Jesus, and that we should make no distinction among them (see Qur'an 2:136; 3:84; 2:285). This means that since each of them preached the true message of God, it would be wrong to say we believe in some but not in others.
The prophets themselves were humble servants of God. They did not try to prove themselves superior to others. It would be wrong for their followers to argue over who is superior. Once a Muslim and a Jew were arguing. The Muslim said that Muhammad is superior over all the people. The Jew said that Moses is superior over all the people. When this was related to the prophet Muhammad, on whom be peace, he said:
Do not give me superiority over Moses (This is recorded in Sahih al-Bukhari, vol.4, p.410, Arabic- English edition).
He also said "None should say that I am better than Jonah, son of Matta" (ibid, p.413).
He also instructed,"Do not give superiority to any prophet among Allah's prophets" (ibid, p.414).
Once the prophet was asked, "Who is the most honorable among the people?" He replied, "The most God-fearing". When he was asked to name a specific individual, he replied:
The most honorable person is Joseph (i.e. the son of Jacob) (ibid, p.390).
This humility was shared by other prophets too. The prophet Jesus, on whom be peace, is reported to have said:
I tell you the truth: Among those born of women there has not risen anyone greater than John the Baptist (Matthew 11:11).
But John the Baptist was also humble. He did not claim that greatness for himself. He spoke of a greater one who was to come after him. He is quoted as saying:
After me will come one more powerful than I, the thongs of whose sandals I am not worthy to stoop down and untie (Mark 1:7).
When God sent the angel Gabriel to take the prophet Muhammad to the Aqsa Mosque one night, the prophet, on whom be peace, led the prayers there, and the other prophets followed his lead. He also related the truth that on the Day of Judgement he will lead the banner of Praise under which will be all the other prophets. But the prophet Muhammad did not boast about this. He instructed Muslims that they should not praise him as the people praised Jesus, son of Mary. He said:
Call me a slave of Allah and His Messenger (Bukhari, vol.4, p.435).
What is important is not to try and prove one prophet superior over another, but to believe in both of them. The prophet Muhammad, on whom be peace, said:
If a man believes in Jesus and then believes in me, he will get a double reward (ibid. p.435).