The book, A People's History of Science by Clifford Conner, goes on and on for pages with one criticism after another, saying that Plato and Aristotle ruined the practice of science, transforming it from an empirical practice of learning from nature to a purely abstract, theoretical study that was totally divorced from reality. The book essentially blamed the stagnation of science for the next several hundred years on their influence.
Here are a few quotes to try to summarize it better:
On Plato:
Plato adopted this kind of geometry [without reference to measurement] as the basis of an 'independent world created out of pure intelligence.' [...] Under the influence of Plato's disdain for anything 'contaminated by practical uses,' [arithmetic] fell into disrepute in the elite intellectual circles of the Greek world. [...] [Plato's ideology] certainly played a significant role in a two-thousand-year retardation of scientific thought--arguably the greatest damage any scientific elite has ever inflicted on science in all of human history. [...]
On Aristotle:
The intellectual elite of the European Middle Ages looked to Aristotle as the ultimate authority on all aspects of natural knowledge. Disputes over scientific questions were not resolved by appeal to observation or experiment, but by poring over the Philosopher's sacred texts [...] Aristotelianism represented a very long detour in the history of science. It was thought to have solved all of science's general problems, but 'the first task of modern science after the Renaissance was to show that for the most part these solutions were meaningless or wrong. As this process took the best part of 1400 years it might be argued that Greek science was a hindrance rather than a help.'
I would take everything in that book with a healthy grain of salt. The author's general thesis and agenda is not really what the whole of the history of science community ascribes to by a long-shot. That does not mean that some of the points he makes about the failures of conventional "great man" histories of science are not shared, or that there isn't a large literature that studies the more hands-on activities that he values, but to go from that to his conclusions is a big leap indeed.
To argue that without Plato or Aristotle we'd have some kind of more advanced understanding of science/nature sooner is pure counter-historical speculation (of dubious value). It imagines that without Aristotle the intellectual elite of Europe would have done something better over that period — I mean, who knows. This is not really the kind of questions that a mainstream historian of science is going to think are the right ones to ask, much less imagine they have answers to, in my experience.