We can all agree that they are both quite awful, but historically, which would you say has done more damage to Humanity?
In terms of damage done divided by time, communism is probably the biggest offender of these three.
Turning to Christianity and Islam in history, Islam spread more often by the sword. The early-Muslim Arabs formed themselves into a military class whose self-appointed purpose was to spread God's new revelation (and their own divinely appointed rule in God's name) across the world by conquest.
Christianity more often spread by co-opting the rising early-medieval 'barbarian' kings who liked the Latin or Greek culture and trade advantages that Christianity brought. The rising kings also appreciated the fact that Christianity and the church supported centralized Roman-style kingship. That fit into the kings' own agendas as they struggled to dominate traditional quasi-democratic warrior aristocracies (who often championed the old Germanic or Slavic faiths).
But both religions ended up suppressing and ultimately trying to eliminate earlier traditions, and both quickly split into sects that contended endlessly among themselves.
In terms of total damage done, I don't see any vast difference between Islam and Christianity back in medieval times.
In modern times, from my Western secular point-of-view, Islam is doing more harm. That's because it remains a much stronger religion than Christianity and much more medieval in its outlook. Traditional 'Christiandom' has been greatly weakened, first by the revival of ancient skeptical doubt during the renaissance, and then by the rise of science and its accompanying rationalism since the 17'th century. The 18'th century industrial revolution just welded that change into place and effectively created a new and unprecedented kind of civilization.
That new society is mow globalizing, being eagerly adopted by the always-astute east Asians, albeit with local variations influenced by their own Asian traditions. There's often a note of Confucianism to their versions of modernity. We see it in the Chinese Politburo/Emperor, in the Party/Mandarate with their formal ladder of advancement, and in the dominance of filial family business dynasties among the overseas Chinese.
And that globalization is meeting its strongest resistance in the Islamic world, which seems torn asunder internally by its own simultaneous attraction to and revulsion against the new civilization of global scientistic secular modernism.
It's an unfamiliar position for their proud and divinely self-assured civilization to find itself in, not unlike the situation of the Byzantines and Sassanids that were conquered and then culturally swallowed up by spreading Islam in the 7'th and succeeding centuries. It shouldn't be surprising that many of the more religious Muslims try desperately and violently to fight it, nor should it be surprising how seamlessly defense of religion and of cultural identity blur together.
