The difference between a sperm cell and a zygote is the chromosome count. The chromosomes determine who is a human and who is not. A zygote has all the necessary chromosomes. A sperm cell does not.
This is an oversimplification, common for laymen. They both have the same number of distinct chromosomes (hopefully), the zygote simply has two copies. We say that the zygote is diploid and the gametes (sperm and egg) are haploid to describe this difference. That doesn't mean that the diploid organism is 'more alive'. When you look at the evolution of plants, the more primitive plants such as mosses and liverworts were (and are) actually haploid-dominant in terms of their life cycles. Any moss that you see growing around you is all haploid tissue, with the sporophyte (those weird brown threads) being the only part that is diploid. Eventually, as plants evolved more and more the haploid part of the life cycle was reduced, until now the opposite is true: the flowering plant tissue that you see is diploid, with the only haploid tissue being within the pollen and ovules. Fungi also sometimes have haploid-dominant life cycles. The number of copies of chromosomes doesn't indicate advancement; there some plants with extremely high levels of polyploidy.
Because of the way that humans have evolved, ploidy overlaps well with our ethical definitions of what 'human' is, but step outside of our species and you'll see that it's just a happy coincidence. Nature often does quite interesting and complicated things with chromosomes that would defy our staid expectations.