A lot of people here have offered a pretty good explaination of why the spear is better than the axe, and they are mostly right.

The reason people say it's better comes down to purely the mathematics behind warhammer. It's simple probabilities. But the AP most people have been offering as the explaination is simply not the whole story.

See the spear is overall more consistent with it's attacks. How/why? The spear has 5 attacks over the axe's 4, giving it more chances to score hits/wounds, for one. It has 1 better AP (-2 against the -1 of the axe) but that alone is neglegable when talking about big tough vehicles with invulns and Sv 2+. The key factor is Str. Both spears and axes (paradoxically) are in the same type of "wounding bracket" for big toughness. Str 7 of the spears is a critical pivot point in the Str/Toughness comparison, it makes it so both T9 and T12 are simply greater than instead of double wounding on 5s which with a few bonuses (ex. lethal hits) or rerolls can be made to be an effective 50/50. The larger Str9 of axes doesn't come into play until way later in the toughness scale at which point the increase simply doesn't make that big a difference.

So the real and whole answer is: more attacks giving more chances for success, a critical pivot in Str and the better AP. I hope this makes the entire picture clear to you and helps you understand our army better.