Nietzsche's notion of slave morality @Ross Campbell
One reason for Nietzsche's contempt for Christianity is its positing of the meaning of this life in a beyond (a crude form of Platonism), in an idealized afterworld, thereby slandering this world, the only world, in all its richness, strangeness, creativity, beauty, terror, etc. Moreover, that idealized world is designed to rob our normal drives of their innocence and to invert the supposedly "natural" hierarchy among human beings, privileging the weak, the resentful, the numerically superior mediocrities over the ascending, joyful, yes-saying creators.
His criticisms definitely seem to rely on caricatures and straw men. I do however think there's quite a bit that's compelling in his analyses, not only of Christianity, but of the modern, secularized Western world which has rejected Christian metaphysics while clinging to its (in Nietzsche's opinion decadent) values and assumptions.
He did distinguish between Jesus the man and teacher (sharing many of the positive views of Jesus that you highlighted earlier), whom he grudgingly admired even while remaining critical of his ultimate vision, and the organized system of Christianity which came to dominate Europe not only politically, but mentally and spiritually. He seems a bit similar to Kierkegaard in that regard although I'm not too familiar with the latter's work so I can't speak with confidence.
I think he interpreted the uniformity of modern science and the egalitarianism of modern democracy to be symptomatic of that lingering Christian influence: The result is a world composed of an indistinct mass of petty human beings consuming mass-created products while boasting of their "progress" and "freedom" and "individuality" etc. He saw the extreme, presumably Christian-inspired leveling coming and tried to formulate the rudiments of a counter-movement. He's a dangerous thinker for sure.
Not sure if that adds anything; it's a pretty standard take. Basically, Christianity does a number on what Nietzsche's takes to be "life" and this is not due to later perversions of a corrupt institutional church - it's right there in the words and deeds of Jesus. (I think this is an interesting debate and I'd like to see it addressed by competent scholars.)