Different species do have different levels of protection, and different lineages tend to employ different methods of protection. For example elephants have numerous duplicates of cancer suppression genes, whereas naked mole rats produce a variant of hyaluronan which prevents tumor formation. When compared to other great apes, Humans seem to be worse at both layers of defense.

It's worth noting though that humans also have much higher levels of exposure to many carcinogens than most animals, and we screen for cancers at a much greater rate for humans, so just because a species has lower cancer rates doesn't necessarily mean their cancer defenses are better.