Great question. The first part of your question about his influence on Christianity is rather simple in the fact that it is generally agreed upon that Apollionus of Tyana lived and preached some time after the historical Jesus was already executed. It's somewhat disputed over what exact years Apollionus lived through, but generally historians agree it was the second half of the first century, some 20-70 years after the Historical Jesus died.

Now you are correct to assume their extreme similarities in both their life and in the way their followers worshiped them after their deaths. However the two groups hated each other. Christianity spread much faster and farther than those of Apollionus and they frequently condemned the teachings of his as fraudulent (which Apollionus' followers accused Christians of the same thing). For sources, primarily all we have are the writings of Philostratus’s who wrote a multi-volumn account of the preacher's life around 200-230 CE, which we can understand came over a century from when the last of the "biblical" Gospels (John) was written (around the year 90).

A really easy to read pop history book called How Jesus Became God: The Exaltation of a Jewish Preacher from Galilee by a highly respected scholar named Bart Ehrman actually discusses this in pretty great detail. Here is a section from that book:

Apollonius lived some years after a similar miracle-working Son of God in a different remote part of the empire, Jesus of Nazareth. Later followers of these two divine men saw them as being in competition with one another. This competition was part of a bigger struggle at the time between paganism— the forms of religion supported by the vast majority of everyone who lived in antiquity, who embraced a variety of polytheistic religions— and Christianity, a newcomer on the religious scene, which insisted that there was only one God and that Jesus was his Son. Christian followers of Jesus who knew about Apollonius maintained that he was a charlatan and a fraud; in response, the pagan followers of Apollonius asserted that Jesus was the charlatan and fraud. Both groups could point to the authoritative written accounts of their leader’s life to score their debating points...

Modern scholars have debated the significance of the obvious connections between Jesus and Apollonius, but it is not merely a recent debate.

From this, it should be reasonably understood that more-so than trying to see how one influenced the other (which it is more likely understood that Jesus' teachings were somewhat stolen by Apollionus since all four of the traditional Gospels were completed by around the year 90), but that the two religions saw a major division between the two, one that lasted for centuries. Hope this helped.