I don't know why, but riding up seems harder to me.
However:
I try to never ever get off my mntn bike on a hill if I absolutely don't have to (i.e. I fall or my bike starts rolling down the hill backwards).
I walk up hills a lot more often when I run.
My mental state is much different when I'm riding in a race as opposed to running. I actually have a chance to place mntn biking and I know that any time I get off my bike I'm going to lose precious time.
When I'm running, there's times I can walk up the hills faster than I'm running--so why waste the energy?