Buddhism is more so a philosophy as opposed to a classic religion. Therefore I believe it's possible for both to exist in harmony. You can be Christian and still practice elements of Buddhism. My greatest thought on religion is that inclusivity might help drive spirituality. I may believe what I believe, but I also deeply respect what others believe as well, and neither is concretely right or wrong. The connection and values of a spiritual force is all that matters.
Having grown-up in a household of comparative religion I saw similarities between the major religions from an early age. Likewise I was also constantly criticized by those around me for having too inclusive of a view. I've been told I was wrong for being Christian and handed rosary beads from Catholics who insisted it was the only way to pray. When I think just praying in general is a step in the right direction...
The similarities in the Buddhist and Christian texts are astounding. Jesus lived 500 years after Buddha but his teachings are remarkably similar. Some historians have suggested that Buddhist principles could have traveled to the Roman Empire, or Jesus may have spent time in India during the less documented parts of his life in his late teens. But a more substantiated answer may be that they just had highly similar religious experiences, or "ah ha!" moments.
Buddha's moment was after a religious quest that lasted six years and resulted in enlightenment under a Bodhi tree. For Jesus that quest was with John the Baptist into the wilderness. There's a possibility that all religions are based off the same historical events or principles, and as that word was carried from continent to continent it was culturally adapted and evolved into the varying religions we see today. Hence the similarities in Abrahamic religions.
Here is a small sampling of similar texts, 100's more comparisons are listed in Marcus Borg's book "Jesus and Buddha: The Parallel Sayings":
Jesus: "Do to others as you would have them do to you." -Luke 6:31
Buddha: "Consider others as yourself." -Dhammapada 10.1
Jesus: "If anyone strikes you on the cheek, offer the other also." -Luke 6:29
Buddha: "If anyone should give you a blow with his hand, with a stick, or with a knife, you should abandon any desires and utter no evil words." -Majjhima Nikaya 21.6
Jesus: "Why do you see the splinter in someone else's eye and never notice the log in your own?" -Matthew 7:5
Buddha: "The faults of others are easier to see than one's own." -Dhammapada 18.252