In Book 9 Adam sounds pretty good when he decides to die with Eve, but are there problems with his logic as well? Does Adam "fall" as badly as Eve?

Adam loves Eve, and so, by joining her in eating the apple, sacrifices his own happiness for love. This, in itself is good act, motivated by love. A true humanist would say that Adam is acting freely and he has done a good thing. Milton, however, shows that even good acts are evil and corrupt if not done in line with God's will. Adam is disobeying God and no matter what he does outside of obedience, it will be bad.

Out of context, the two fall together, as they have both failed to abide by God's rules. None-the-less, many people see Adam's actions as more consequential than Eve's because it was Adam who should have stopped her.