Please explain. It seems to me that Neitzsche was dead on regarding what morality is when God does not exist.
Well, since you assume God does exist, I'm not sure we can establish this, but the ability of millions human beings who don't believe in God to nonetheless be constrained in their behavior and/or altruistic/self-sacrificing seems to make Nietzsche's thesis silly.
What measures are you using to determine what "better" is?
The Ten Commandments will do I suppose, if you accept scott's view that they are moral laws. Do believers obey them more than non-believers? Well, maybe a little, or maybe not, but I'd argue not so much more as to qualify as "better." Plenty of Christian (and atheist, Jewish, Buddhist . . .) liars, coveters, adulterers . . . to go around.
Where does Christianity say human beings are "shit"? After all, we still acknowledge that we are made in the image of God, which kind of qualifies us as not being such. What Christianity claims is that we are in rebellion against God; but considering God didn't simply erase humanity or even decide not to create us, then we must have some value even from the divine perspective. The problem is rebellion, not our value as beings.