A funeral is doing at least three things simultaneously, and traditions weight them so differently that comparing the ceremonies without separating the functions produces nonsense.
It disposes of a body, which is a practical problem with a deadline. It settles the status of the dead person, which is a claim about metaphysics. And it reorganises the living, who now stand in different relations to one another and need that stated publicly.
Judaism and Islam weight the first and third and are deliberately austere about display. Both bury quickly, both use plain wrappings identical for rich and poor, and both traditions contain explicit statements that an expensive funeral is a discourtesy, because it shames families who cannot match it. The rabbinic sources record a deliberate reform to this effect, and it worked.
Hindu practice weights the second heavily and assigns the work to a person. The chief mourner is not a spectator; over the following days his offerings are understood to construct a subtle body in which the deceased can travel, and until that work is complete the dead person is in an unfinished and somewhat dangerous condition. The ritual is a task with a product.
Catholic and Orthodox funerals are offered as prayer for the dead, on the premise that the living can still assist them. The Reformation rejected that premise directly, and Protestant funerals became proclamation addressed to the living instead. The two look superficially similar and are doing opposite things, and this remains one of the sharpest practical divides in Christian life.
Buddhist funerals across most of Asia transfer merit to the deceased rather than petitioning any power on their behalf. The mechanism is different from intercession even where the outward form of chanting monks and offerings looks much the same.
One general caution. Nearly every tradition's funeral rite is older than its own doctrine of the afterlife, and has been reinterpreted more than once to fit later theology. Deliberate burial in the archaeological record predates any recoverable belief about it by a very long way, and confident inferences from grave goods to doctrine are a great deal less secure than popular accounts imply.