In Buddhism, you can believe in a god if you want to or not. Its a choice for each person. But I would say Buddhism is close to rational. More so than religions.
Buddhism is considered a philosophy by its followers, not a religion.
Because Buddhism is a philosophy and not a traditional god-fearing religion I do think it's quite rational. I can't accept reincarnation so it's not exactly my cup of tea, but Buddhism is certainly not a threat to human civilization. I confess, I don't know enough about Jainism to express an opinion.
I certainly feel that way about Buddhism, but Jainism relies on one basic concept that I don't view as rational. That view is the eternal soul. This seems contrary to common sense to me, since the population has increased dramatically over the last several Milena. It makes no sense to say that each of us has an eternal soul, since that soul would have had to exist from the beginning. Such a concept would be inconsistent with a growing population, in my opinion.
It should be noted that Buddhists can believe in god. I also noticed that another answer included the idea that Buddhists don't consider Buddhism a religion, but they do view it as a philosophy. Views are nice, but definitions are much more concrete. Therefore, I must ask this question about Buddhists: Do they have a system of beliefs that they practice which they feel or think are true? If the answer is yes, then Buddhism is by definition a religion.
Buddhism doesn't say there are no Gods, of course there is (There are many living things in this universe such as, gods, demons, ghosts, Brahma's, spirits, aliens etc etc) its like we humans, But a different group of living beings with different patterns of existence) but Buddhism clearly says there is no such 1 particular god called the ever supreme ultimate creator of everything. Instead Buddhism says everything in this universes is based on the universal law of cause and effect. So even gods are subjected to this law of cause and effect.
I am posting my answer from a different question concerning whether Buddhism is a religion - because I hope it my help some with an understanding of differences between Buddhism and atheism. Also, may Buddhists do believe in G-d, and it is important to understand more about Buddhism than possible to write in this space to discuss the concept of G-d in Buddhism.
Buddhism may be considered a religion and / or a philosophy. As a Buddhist I consider it to be both a religion in and of itself as well as compatible with other religions and even non-religions. Of course there are subtle differences that a Christian for example would practice as compared with atheist. Of course, a major difference for atheists would be the belief in nihilism which is contrary to Buddhist practice, but of course this would not prevent an atheist from practicing a moral or ethical life based on Buddhism. At some point I suppose it breaks down. Same for a Christian, Muslim, Jew, etc. but with some different subtleties.
It is also my understanding that eastern Buddhists more often consider it a religion, whereas western practitioners are more likely to take on the 'philosophy' view, perhaps because more western practitioners include ideas from their Judeo-Christian roots...