The difference is that Jewish is not based on history. There is sufficient proof of uour presence in Israel to satisfy readings of Torah. The main tenets of my faith is the existence of G-d and His Covenant with my people.
And the covenant is a historical reality. If the events as described in the Torah didn't happen then there was no covenant.
My understanding of Xtianity is that it is based on Jesus being the son of G-d and having walked the earth. If the very evidence of places and times where he is alledged to have existed is destroyed, it reduces to story to, well, a story. There is virtually no extra-biblical evidence of Jesus's existence.
The existence of a historical person doesn't need to be confirmed by extra canonical sources. The authors of the NT, taken as authors with the faith aspect bracketed out, make it quite obvious that Jesus existed. Whether or not his claims of divinity are believable is another matter. Doubting his existence is really about as unreasonable as doubting Hannibal crossing the Alps or Alexander making it to India (both of which people believe on less evidence than the existence of Jesus).
The gospels are a circular argument if taken in a vacuum. The physical evidence of the Jewish Temple, and of the Jewish presence in Israel at that time help put the gospels into context and at least lead some form of credence to the stories. Remove the physical evidence and what are you left with?
Well, since Catholicism and Eastern Orthodoxy aren't sola scriptura faiths you are left with the witness of both Scripture and Sacred Tradition.
As I said, the removal of the archaeological finds are tantamount to theft. Doing so makes it more difficult to feel connected to those who have gone before us in the faith. But it doesn't really effect the question of Jesus' historical existence.
