Hinduism teaches that if you exist, you will always exist. If you do not exist, you will never exist.
The Bible teaches that if you exist, upon death you will cease to exist. Jesus compares this to sleep, speaking of Lazarus. Lazarus remembers nothing upon waking from the sleep of death, after his resurrection.
Hinduism teaches that all beings are a part of God, but God is greater than the sum of these parts.
The Bible teaches a division of creation, that God is separate from angels and mankind, which are separate from each other (and animals), and that God is greater than all.
Hinduism is a collectivist faith - One man may reincarnate as another woman, as another man, as another being alltogether. They will be different and the same.
The Bible communicates an individual faith - One man is born once, will die once, and may be resurrected.
Hinduism believes that the Ego corrupts choices of free will, but that the ego may be transcended.
The Bible treats egotistical decisions as a part of normal human baseline-function, and all decisions are subject to judgement, though you may repent for bad ones.
- Dane Curley