Whereas religion often functions on a single-choice basis. In Christianity, the benevolent God says "Love me, believe in me, or you will go to hell." Political opinion is based on critical thought, not blind faith. Politics does not use fear to brainwash individuals into believing a set doctrine, it does not give ultimatums on pain of horrible suffering for eternity.
I wouldn't say that religion is more "harmful" than politics. It would be more accurate to say that religion is more "influential". In politics, decisions made by politicians are often defined as "ideas" or "deals" or "plans". These items tend to be open to tweaks and modifications and are accepted by popular voting most of the time. In religion though, the same concepts are called "beliefs", and generally people will do anything to protect them and prevent them from being modified - even fight and die for them!
Both politics and religion can be used as tools to inflict harm on individuals and societies, regardless of the stated morals and objectives of the respective religious or political ideologies. The point is, both can be used to do a lot of good as well. I think, as societies and nations become more 'civilized' the amount of harm that can be inflicted by either tends to decrease. It is unthinkable for instance that we would have another Stalin or PolPot (non religious political leaders that inflicted more harm on their peoples in the 20th century than even Hitler did on Germans). Sure religion have also caused conflicts and but secular conflicts driven by secular totalitarianism have killed far more people than religious conflicts.
Another point I would make is that religion is a very powerful force that generally reinforces virtuous behavior in people, while politics is less likely to do so.
Both religion and politics can be extremely harmful if taken to absolutes and extremes. Historically, religion has been responsible for the majority of fanaticism, but the 19th and 20th centuries proved that secular ideologies such as nationalism, communism, fascism, etc could be just as violent and senseless when extremists took the reigns.