No one who has ever had a baby chimp climb trustingly into her arms (I have) can doubt that Pan troglodytes is the nearest living relative to Homo sapiens. But how close does that make us? Should we, as some influential scientists and philosophers have argued, see chimpanzees as fellow humans and accord them the same rights? Or does science support the assumption of human uniqueness that has prevailed through most of civilisation?

As his title suggests, Jeremy Taylor is firmly in the second camp. A TV science producer, he was driven to distraction by a stream of documentaries showing cute chimps displaying apparently human traits such as empathy, tool-making and language. Egged on by a tendency to anthropomorphism, some primatologists have argued that the difference between chimpanzee and human cognition is simply a matter of degree. Taylor is having none of it: "To call the difference quantitative between alarm calls, food-specific grunts, whoops and Shakespeare; between night nests and twig tools, and the A380 passenger jet; and between retribution and food sharing and Aristotle and Mill is, to my mind, stretching a point, and a bit of an insult to human ingenuity and culture."

At a superficial level, science supports the chimps 'R' us hypothesis. In 2005, scientists published a letter-by-letter comparison of the chimpanzee and human genomes, with an overall similarity of 96%. For comparison, studies of the human genome now put the similarity between any two individuals at between 97% and 99%.

The simplistic implication was that a small handful of genes made us big-brained, hairless, upright, long-lived and able to compose blank verse, baroque opera and the theory of relativity. The reality has turned out to be much more complex. Yes, there have been single-letter mutations that have changed the function of some genes. But much of evolution depends on grosser forms of variation in which whole genes, or parts of genes, became duplicated, moved to other chromosomes or were lost altogether. Moreover, subtle changes in how they are controlled mean that the same genes can be read in alternative ways to produce a variety of different products. New research shows that all of these mechanisms have been at work to drive humans and chimpanzees apart at an accelerating rate since they diverged from a common ancestor. Taylor minutely documents the way that apparently small changes have had disproportionate consequences, particularly in brain development and the immune system.

While the jury is still digesting this barrage of hard biology, Taylor brings on his star witness in the form of Betty the New Caledonian crow. Betty knocks spots off chimpanzees when it comes to making and using tools. Her cousins the scrub jays re-cache their food if a potential pilferer was watching when they hid it. If corvids have such "human" skills, should we give them human rights too?

Taylor gives no more than a dismissive aside to chimpanzee language studies, most of which he describes as "ridden with wishful thinking, over-exaggeration and even downright fantasy". Though this does not make for a scrupulously fair presentation of the evidence, his approach is enjoyably combative and certainly succeeds in mapping the biological, behavioural and social landscape that divides us from our next of kin.

• Georgina Ferry's Max Perutz and the Secret of Life is published by Pimlico.