Since there is a Jewish Buddhist movement, here is a list of ways in which (Theravada or early) Buddhism and Judaism are, as I understand, more similar to each other than either is to Christianity:
- In both, though there are things on which most members of each religion agree, there is no firm dogma, because the spiritual goal (experiencing God or Nirvana) is thought to be beyond mundane human thought. Individuals are free to explore their own spiritual feelings and beliefs, and to develop their own understandings. Prophets, Messiahs, the Buddha, and monks are people who may have had an especially clear or rich spiritual experience, but they are not God(s) themselves. Said another way: both religions are more orthopraxic than orthodoxic (i.e., less faith-based, more focused on what people do and experience than on what they believe).
- Absolute reality, God, etc. is usually thought to be some kind of unity or single substance, not a trinity, a hypostatic union (hybrid God-man), etc.
- Both are/were largely aniconic (Buddhism was in the early days) and prohibit giving anything a higher status than God or nirvanic beings.
- Like devas in Buddhism, early Judaism seems to have acknowledged polytheism (e.g., El becoming YHWH, “You shall have no other gods before me,” etc.), but neither made polytheism central to their religion.
- Hell is not forever. In Judaism, hell is more like Catholic purgatory and lasts only a short time, so that God can teach sinners a lesson. Those souls who are too bad to be redeemed are either destroyed by God, which seems much more compassionate to me than eternal torment, or continue to exist in a remorseful state. In Buddhism, the length and depth/badness of a hellish life varies based on one’s karma, with the worst hell being called avici. Both also find rebirth/reincarnation possible.
- Both generally lack a notion of original sin, though in Buddhism, the mind that is reborn has typically had many past lives and has accumulated many both good and bad traits. Both see people as a mixture of good/selfless and bad/selfless impulses, and see a Middle Way-type balance to be necessary for successfully living in the world (e.g., a person has to be a little selfish in order to have food to eat, to do a job, etc.).
- Less focus is placed on external forces (e.g., the devil, praying to angels or saints, God(s) taking physical form, etc.), which are usually considered to be metaphorical. Unlike how Christians often interpret it literally, the oft-quoted line from Genesis 1:27, that man was made in the image of God, is usually taken in Judaism to mean that human’s nature, essence, or capacities for things like reason and intuition are similar to God’s, not that God literally has a human-like (or any corporeal) form.
- Both Buddhism’s precepts, the Brahmaviharas, etc. as well as Judaism’s kosher rules are concerned with how to kill animals as sparingly and humanely as possible. In both, the brief five-to-ten precepts/commandments are just a categorization or introduction to a much longer set of vinaya/commandments about many aspects of life.