What makes the result special is Bragg's unusual relationship to his subject. With a background in the arts, but a keen interest in science developed later in life, he approaches it as an outsider. This gives him a freshness which is impossible for those more familiar with individual trees than the appearance of the whole wood. His gentle probing, and the selection of material (much more here than in the broadcast versions), addresses exactly the questions about science and scientists that interest outsiders. Bragg asks what drives the great scientists, rather than just listing their achievements.
The great danger with this approach is that, as the title implies, it suggests that science progresses as a result of the work of isolated geniuses. I do not agree. With the exception of Isaac Newton (always an exception), it is hard to see how the development of science would have been much delayed by removing any of the individuals analysed here from the scene. Even Charles Darwin was only pressed into publishing his theory of natural selection when he learned that Alfred Russel Wallace had come up with exactly the same idea. And there are many things to annoy the informed reader, not least the hackneyed presentation of Darwin as a teenage wastrel who cared nothing for science and fell into his berth on the Beagle by luck. In fact, Darwin worked diligently at university, although in areas that interested him (such as geology), not the subjects he was supposed to study (medicine and theology).
Nevertheless, the device of hanging the story of science on the shoulders of great names works as a piece of storytelling, just as the (now unfashionable) device of hanging history on the shoulders of kings and queens works. It is a version of the truth, but not the whole truth. And, like the story of kings and queens, it is an excellent way to get started on the subject.
The audience Bragg is addressing won't care too much about what Newton really meant by his famous remark about seeing further by standing on the shoulders of giants; but they will get some insights into both the subjects of the book and the modern scientists over whose shoulders we look. The result is a satisfying package which is easy to read, a delight to dip into, and may just encourage a few casual readers to probe more deeply into the wonders of science.