Nirvana is basically heaven, not eternal death. Reaching Nirvana means that you have ended your cycle of reincarnation and exist in endless peace.
Not all forms of Buddhism believe in endless reincarnation, or reincarnation at all. There were many Buddhas and there continue to be more. Siddhartha was just one Buddha.
You can't really compare Buddhism to Christianity- it just doesn't work. Buddhism is more about a road to enlightenment and living a peaceful existence as to not harm another being. Christianity is focused on what happens after death and living a life to make sure that you end up in heaven.