But why there is so much difference between MPC and BAA predictions?

I don't know ... but the predictions come from a formula which is basically

M = M0 + 5 log D + k log r

where M0 is the "absolute magnitude" (taken as the comet being 1AU from both Sun and Earth), D is the distance from the Earth and r is the distance from the Sun. k=5 for asteroids, around 10 for short period comets which have been around for a while and around 15 for "fresh" comets which have only newly been perturbed into orbits which bring them into the inner solar system.

Clearly the predicted magnitude depends on the value of k used.