Buddhism is a practice of which brings about realisation aka awakening. There is no attainment to be noted in mentioning of which nirvana applies as being a means to an end, so there is actually nothing attributed by way in which comparatively, a Christian seeks heaven. There remains no heaven for a Buddhist to enter nor any hell to flee.
I've argued this before that Nirvana is essentially uncaused, and it just happens, but under this then Buddhism would be pointless as a philosophy, because nothing contained within the philosophy would lead to Nirvana. Being a mass murderer would be just as likely to lead one to Nirvana as would the path of Buddhism.
And not all sects of Buddhism don't believe in the concpets of Heaven and Hell, I seem to recall some sects of Mayahana that hold the belief of Heaven, Hell, demons, and angels so to speak.
It's true in which compassion can leave a feedback through cause and effect motivating one to continue by the feeling such acts can generate, yet even so, nothing remains guaranteed by compassionate action as opposed to guarantees made through biblical scriptures through a course of action leading to spiritual rewards.
I would agree, there is much more of a contextual premise within Buddhism, rather than the gaurantee made by the Bible.
Even so, Christianity in it's modern, mainstream form doesn't neccesarily gaurantee anything by compassionate actions either. It actually says exactly the opposite, that your place in heaven is not gained by compassionate actions, but rather by the belief in Jesus Christ, whatever that means to each person.
However, I personally would argue that this is not the doctrine that Yehoshua taught himself, and that he was actually vehemently opposed to doctrines such that are attributed to him as they are today.
I would argue that Jesus would have been more akin to some of the more esoteric aspects of Tibettan Buddhism myself. Just my .02 cents.