Perhaps it is that Buddhists emulate Buddha, and Christians emulate Jesus Christ, however Buddha and Jesus did not emulate anyone -- they led the way.
This is the whole point. Buddha did not follow an ideal, he lived it. The same goes for all leaders - 'Buddhism' or 'Christianity' then defines the way they demonstrated - the attempt of people to follow the way as emulated in the lives they witnessed.
I disagree with the notion that Buddhists would murder the Buddha, or Christians would murder Christ. This may well be the 'way of the world' which seeks to serve itself, rather than a higher cause, but in so saying one should discriminate between common opinion and the unspoken faith of true believers.
To assume that to be Christian is to be Christ, or to be a Buddhist is to be Buddha, is asking for your neighbour to be perfect.
Christ lives in everyone - "In him was life; and the life was the light of men. And the light shineth in darkness; and the darkness comprehended it not." (John 1:4-5) - and who is Buddha but an enlightened being?
The world seeks to put out the light of Truth so that its own light is the only illumination - a glimmer against the 'supernal darkness' - darkness is a condition of self-willed ignorance, and "empty vessels make the most noise."
But they also serve, who only stand and wait." Milton.
The Word is Truth, and Beauty - the world is hollow, but with a seductive glamour. Meanwhile there are those who attempt to live the beatitudes, and they are reviled by the world, silenced by the world, ridiculed by the world ... and ignored ... the world makes a big deal of the murderer, and proclaims its shock and its horror and revulsion ... but more people die daily at the hands of the world, killed by callous indifference ... the world lives in utter denial of the reality of itself, for were it to look in the mirror, were it to listen to the voice of faith, it would slink away in the shame of its inhumanity.
Worry not, Jesus said:
"I am the good shepherd, and know my sheep, and am known of mine."
When He speaks, those who carry Him in their hearts will recognise His voice.
God speed the day,