While the teaching of compassion for others is common to both the Buddha and Christ there is no historical evidence that Christ knew anything about the Buddha or his teachings.
It should be noted that the Buddha never claimed to be a god, the son of a god, or anything along those lines. Buddhism is purely experiential. The Buddha taught the "means" he used to reach a state of enlightenment. It's up to the individual practitioner to test the means the Buddha, and other Buddhists teachers, teach and see for themselves if they work in their case.
It's hard for most westerners to understand, but Buddhism really isn't a religion. The Buddha is most like a doctor, and his teachings are like a prescription that you take and see if it works for you.