Are religious rituals or religious beliefs more important?

The answer to your question depends almost entirely on which religion you are talking about! In Christianity, especially in the protestant tradition, beliefs tend to be valued more than rituals. During the Protestant Reformation and beyond, faith took on an extremely important role in protestant culture that contrasted with the Catholic Church’s emphasis upon rituals— sacraments, fasts, etc.

Judaism, on the other hand, is considered by most Jewish scholars to be a religion that places a far greater emphasis on practice than on belief. In observant Judaism, the most important element of religious practice is the fulfillment of mitzvoth, or commandments that connect the Jewish practitioner to a relationship with God. While some Jewish thinkers like Maimonides did place a significant emphasis on belief, most observant Jews value ritual much more highly, and many Jewish thinkers agree that one can be a religious Jew and not even believe in God! An often quoted principle among the observant is “Na’aseh v’nishma,” or we will do and then we will understand--- this Torah verse flips the expected order of understanding before doing, and is often interpreted as indicating that deeds are more important than intentions in Jewish religious practice.

Similarly, Buddhism tends to be a religion of practice rather than belief (a notable exception to this is the Chinese and Japanese sect of Pure Land Buddhism, which places an enormous amount of emphasis on perfect faith in Amida Buddha, which will lead to reincarnation in the Pure Land). The Buddha is famously quoted as responding to a man who asked about the nature of God and the Universe— “You have been shot with a poison arrow--- and now you want to ask about who the shooter was? Work first on pulling the arrow out!” This story is told to bring home the point that Buddhism places more emphasis on the following of the Eightfold Noble Path as a means to eliminating suffering than on any kind of metaphysical conjecture. Indeed, it is very possible to be a Buddhist practitioner in many sects (Zen Buddhism especially) without having any belief in a higher power whatsoever.