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Since Buddhism states: "‘It is impossible, it cannot happen that two Accomplished Ones, Fully Enlightened Ones, could arise contemporaneously in one world-system", the view of Buddhism is those teachings of Jesus that are similar to Buddhism have their source in Buddhism. Therefore, the Buddha is the teacher & Jesus is the student.

Buddhism explains there are many types of liberation of mind (MN 43), which include liberation via loving-kindness & liberation via emptiness of self, the later being the foremost & unshakeable.

Where as the Buddha taught straightforwardly & plainly, which key terms explicitly defined.

Buddhism explains there are many types of liberation/salvation of mind (MN 43), which include liberation via loving-kindness & liberation via emptiness of self, the later being the foremost & unshakeable.

Where as the Buddha taught straightforwardly & plainly, with key terms explicitly defined.

Also, Christianity is fatally connected to the Old Testament of Judaism, which allows killing in many circumstances, such as war & heresy. This is why Christianity has had many Inquisitions.

In other words, Buddhism is strictly 'impersonal' where as Christianity is 'personal', where salvation is based on a relationship between the 'small-self' and a personal god (Christ & The Father). For example, Luke 23:42 states:

In other words, Buddhism is strictly 'impersonal' where as Christianity is 'personal', where salvation is based on a personal relationship between the 'small-self' & a personal god (Christ & The Father). 

For example, Matthew 16:25 states:

Whoever loses his life for My sake will find it.

Luke 23:42 states:

He understands: ‘It is impossible, it cannot happen that a person possessing right view could acknowledge another teacher ― there is no such possibility.’ And he understands: ‘It is possible that an ordinary person might acknowledge another teacher ― there is such a possibility.’

He understands: ‘It is impossible, it cannot happen that two Accomplished Ones, Fully Enlightened Ones, could arise contemporaneously in one world-system ― there is no such possibility.’ And he understands: ‘It is possible that one Accomplished One, a Fully Enlightened One, might arise in one world-system ― there is such a possibility.

MN 115