I’ve been learning a bit about Buddhism for a while now, mainly through Thich Nhat Hanh’s biography of the Buddha, Old Path, White Clouds (which, full disclosure, I have not yet finished). I see a lot of truth in it, but seeing that I’m a Catholic Christian and not a Buddhist, I feel the need to set the two side by side, to prevent any confusion. Of course, I’m no expert on Catholicism, let alone Buddhism, so please correct me where needed in the comments.
The aim of Buddhism is to attain and share awakening (Buddha means “the awakened one”), realising that there is no such thing as a separate self, thereby liberating the person from suffering as well as the cycle of death and rebirth. Realising that all is one, that all things exist in all other things, the selfish thoughts and desires that cause suffering disappear, as does death and rebirth (as the you that dies and is reborn, was an illusion you are now without). [I’m a bit less clear on liberation from death and rebirth, so if anyone could help me, I’d really appreciate it]

The aim of Christianity is God’s aim to draw all of creation into union with Himself in love, through the cross of Jesus Christ, setting us free from all sin, division, and death. In Jesus of Nazareth, God’s love in which He made the whole cosmos is made manifest, shared with us, and offered back to God in thanksgiving. Jesus loves us to the point of letting us kill Him, and still loving us. He offers up our ultimate crime – His own death – as a thanksgiving to God, His Father. Even in our rejecting Him, He is uniting Himself to us. It is the Christian’s aim to let Him.
The Buddhist concept of Annata, or “non-self”, is met by the Christian Kenosis, or “self-emptying”, which are so close and yet so far apart. Annata refers to how all things lack a separate self, while Kenosis reveals a self that exists precisely in its gift, its self-annihilation. The image of Buddhism is Buddha sitting in meditation, and the image of Christianity is Christ crucified.
In Buddhism, it is recognised that all things are interdependent, all things are one, and this reality must be recognised. In Christianity, all things are already one also, being held together in Christ, the Divine Logos, but are also being taken up in Christ into unity in God the Father Almighty. We are created in God’s love, and receive God’s love in Christ upon the Cross, and are united to His crucified love offering us back, up to the Father and out to mankind. We are in the middle of the dynamic, creative, expansive Oneness of the Trinity, in whom we live and move and have our being.

This has helped clear my mind, and I hope it has helped you too. I think thanks to learning about Buddhism, I understand Christianity better, and I’m deeply grateful. And I don’t mean that just in terms of “what not to believe”.
Let me know if you have any thoughts on this.
God bless you :)