Here we go into the common ground and the differences between Buddhist schools and those of Christianity who are conscious of their own spiritual depth. For this purpose, the life and teachings of Buddha (500 BC) will not be described extensively. * Essential points are discussed precisely.

The core of the original teachings of Buddha - which the "Hinayana" Buddhism is still based on – is to liberate oneself more and more from everything that does not belong to one's essence. The desires of the senses and the mind, leading to suffering, shall be recognized as "not belonging to the self" ("anatta"); and shall finally vanish and lead to the state of Nirvana. This can be achieved by an adapted way of life and training, including meditation etc. Especially the later school of "Mahayana" Buddhism - which also made progress, such as the empathy with all beings instead of withdrawal from the world - often misunderstood this concept of "not self". They interpreted it as if no "I" would remain at all after one leaves behind the low, egoistic qualities. So they tend to interpret Nirvana as "nothing" too. Buddha himself, however, even spoke about his highest experiences (ninth step): "And  I ... saw (also) through the misery of the area of 'Neither Perception Nor Non-perception'. In the course of time it became fully clear to me and (I) penetrated into the happiness of the abolition of Perception and Feeling. I have had my fill of it... And so since that time I gain - after full elimination of 'Neither Perception nor Non-Perception' - the 'Abolition of Perception and Feeling' and stay in it; and, after I recognized that all wisely, the influences became exhausted" (Suttam of the Anguttara Nikaya 9, No.41 ...).
In so far one can recognize that Jesus Christ also inspires people to purify their qualities, and to begin with themselves instead of immediately criticising others (see the main text of ways-of-christ.net). He does not identify himself and his disciples with the world or any secular activities, but describes them as not belonging to the world; but - more clearly than in the original Buddhism - as living and working in the world (John 17), transforming the world like leaven.
Anyway, sayings of Jesus and Buddha concerning questions of life show such a large number of similarities that for decades some people thought that Jesus was teaching Buddhism. But this is not correct. We could just as well say he taught another one of the old religions. In our main text it is explained, e.g., that such similarities ('partial accordances') are caused by spiritual realities, which everyone can perceive who has access to them, without copying each other. (...) This is a strong point of the religions - if compared with a materialistic and egoistic society - which they don't use enough. But similarities and contacts between the religions do not alter the fact that they all have their own slightly different paths.
(... updates in the related German page).

However, in Judaism, Christianity and Islam the qualities one has to purify are additionally associated with sins in relationship to God. For one thing, this concerns keeping religious ethical rules; to be more exact, it concerns overcoming all qualities, that separate us from God. Usually there is the conviction - probably among most Buddhists themselves too - that in Buddhism there is no God. Therefore mutual ethical declarations of religions only refer to a "Last Reality" beyond the physical life, accepted by all religions, whatever that means in each of the religions. This is, however, not quite correct. Buddha never stated, that there was no God, but in his time he confined himself to speaking about insights concerning the human way. Buddha answered questions of Hindu priests about Brahma, the creative deity of the Hindus: "I know Brahma well and the world of Brahma, and the path leading to the world of Brahma and how Brahma reached that world, I know this too" - (Digha Nikaya, 13th speech - referring to spiritual experiences, not to simply knowing the books of the Hindus.) 
He speaks about the origin of everything, even of the Hindu deities. So, what is he speaking of? (Obviously for Buddha the origin and the goal were unmanifested. However, the unmanifested Nirvana or highest reality is not "nothing". It is simply beyond human imagination. Note: Christianity, Judaism, and Islam all know that it is of no use - or even forbidden - to make an image of God. (...). The Brahma of the Hindus cannot simply be equated with the Father, taught by Jesus Christ. Brahma is rather one of the personifications of some of God’s qualities, which came up in different cultures in the course of time . In any case, Brahma is not the name of negative forces.
The Gospels and the Revelation describe the "Father" as both starting creation and as being its final fulfilment (Alpha and Omega). He is said to be above creation and its qualities and it was not possible to reach it before Christ. Christian Mystics like Jakob Boehme, stated, according to their authentic experiences, that this God is not only above the creation of the physical creation, but also above beyond and above the "first, heavenly creation". ** The attempt that most scientific books make to compare religions without including those who have had deep spiritual experiences, will not help anyone much. *** Without this it is not even possible to find a language that can be understood on both sides.

The Buddhist Path leads to entering into "Nirvana", beyond the beyond - something which is, for most Buddhists, as 'far away' as the Mystical Union with God is 'far away' for most Christians.**** Nevertheless, Buddhism also teaches that a "Bodhisattva", one " liberated from reincarnations " can come down voluntarily to help the rest of mankind.
Christ ascended to the Father ("And the grave was empty..."; & Resurrection & Ascension), with the promise to come again. With Christ and his way, today a permeation from the highest divine realm beyond everything down to the physical level has become possible.

Rudolf Steiner might be worth mentioning at this point too. He said that Buddha brought teachings about the wisdom of love and Christ then brought the power of love. Here the Buddha is seen as some kind of trailblazer. He who wants to recognize reality, may ask Christ and/or Buddha himself on his/her way!

*) The teachings the Buddha handed down himself can be found in the extensive translations of K.E.Neumann,"Die Reden des Buddha: mittlere Sammlung" (The speeches of the Buddha: medium collection; German; probably also translated into English); in the "längere Sammlung" (long collection) too.
**) For people with theosophical usage it is mentioned that in theosophical terms, to be exact, the Nirvana or Atman is below the "paranirvanic" and "mahaparanirvanic logoic" divine levels.
***) The Christian Mystic Master Ekkehart described his experiences like the Nirvana experience – without using this word -, but the difference was that for him it was connected with meeting God.
****) Returning to God with the essence from the way through the world is on the one hand a return to something, which was already there all the time. On the other hand it is something additional, which was not there before, like two congruent triangles. This paradox can only be understood through deepened mystical experience.