Christ and Buddha are arguably amongst a small handful of men who have had the most influence on humanity over the last two thousand years. Let’s consider Their lives and Teachings. These two men have brought teachings that have profoundly shaped the moral, spiritual and intellectual lives of millions who have followed their Teachings. However some would argue they exemplify two irreconcilably different paradigms, Abrahamic and Dharmic. So have these Great Educators brought spiritual paths that are so divergent that they can’t be reconciled. On the other hand with some closer attention to what we know of their teachings, the historic circumstances from which they have emerged, and how their teachings have evolved through the centuries perhaps they are much more similar than different. Can we have a convergence of two very different traditions or are they irreconcilably divergent?
Comments and questions as you will.
The Buddha's teachings are about as contrary to Christ's as it gets - which shouldn't be a surprise since each set out to resolve different issues and came from very different cultures.
Christ came as the Messiah to reconcile man to God by addressing the barrier between us: sin (and it's consequence: death). He summarized God's Law, his will for us, with just two short commands: Love the Lord your God with all your heart, soul, and mind, and love your fellow man. In fact, so important is love that God is said to be love. Christ exemplifies love through his self-sacrifice for the sake of others. Though he did not desire to suffer and die, he took on that role because his love for God and for us was greater than his concern for himself. We are called to similarly give our lives to God doing good works, loving others. This ultimately leads to reunion with God and to eternal life.
The Buddha was concerned with suffering above all else - how to escape it. It is commonly said in Buddhism that life is suffering - for at every turn there is some degree of unpleasantness. There is some degree suffering in birth, in death, in sickness, in being denied whatever you desire, etc. And, being raised in India everyone believed in Samsara - the cycle of birth, death, and rebirth. So you didn't just have to put up with this suffering once - it is understood as an infinite cycle of suffering. And in order to escape samsara, to reach Nirvana, one must address the underlying source of Samsara: Karma, our moral actions. In particular, existing karma must be worked through and we must not produce more karma (save neutral karma). This means that one must both not do anything bad as well as not doing anything
good.
Furthermore, attachments to others are considered to be a bad thing and a source of suffering and illusion. As such, a practicing Buddhist cannot love in the same sense as what is called love in Christianity. They use the term but it is not really love.
While Buddhism has many sects, the core teachings above are irreconcilable with Christianity and are contrary to it.
EDIT: They also believe there is no soul, which is also irreconcilable with Christianity if taken at face value. You might be able to re-interpret to simply mean that people are always changing or something, but this would still be irreconcilable with God in Christianity - who is said to be unchanging.