The similarity between the Jesus of the gospels and Moses in the Old Testament comes about because the gospel authors, most notably the author of Matthew, wrote accounts that emphasised the similarity. They clearly believed that if Jesus could be shown to be similar to Moses then that would confirm his greatness.
Some of the evangelists missed opportunities, or did not feel that comparisons between Jesus and Moses were so significant. Whereas Matthew says that the father of Joseph was called Jacob, just as in the Old Testament, Luke says that Joseph's father was called Heli. Raymond E. Brown (An Introduction to the New Testament) says there is little likelihood that either is strictly historical, but Matthew is able to use this small point to create a parallel with Moses. The entire nativity story of Matthew goes on to draw a parallel between Jesus and Moses.
John Shelby Spong (Born of a Woman: A Bishop Rethinks the Birth of Jesus) says that Matthew was clearly writing Christian midrash.
The significance is that, even today, there are some who look for this evidence and stare in wonder when they see the gospels describing Jesus in these terms. The evangelists were right to believe that similarities between Jesus and Moses would always be highly regarded.