My limited dealings with Milton Friedman (as a student at U of C and various chance meetings) did not endear him to me. I found him a rather unsympathetic personality. But, as a scholar, from his writing, I learned a great deal. I refer to his writing on policy and political economy. He was always clear and logical and tried to anticipate all possible counterarguments. He did not engage in hyperbole or gratuitous denigration. He was perhaps the most effective popularizer of the ideas of classical liberalism of the twentieth century. There was a lot he did behind the scenes that may emerge over time. He advised many governments, including those of Israel, India, Chile, China and the U.S. Who knows how many millions of people benefited from his advice in the journey from poverty to middle class.
I found his scholarly work frustrating in his concessions to the prevailing methodology. He was a strategic writer. He adopted the medium best suited to get the attention of those who disagreed with him most. As a result, for example, he adopted the Keynesian macro-model and much of his work on money comes to us through that. Its hard to know how much he actually approved of the models he used. But he was a master in dressing up appropriately. His Theory of the Consumption Function is more than that though. In that work he went to the center of the conventional wisdom in econometrics and exposed it for a fraud - there were fatal conceptual errors in the main variables. I believe it is hard to overstate the influence of this work on the economics profession and on Friedman's career. After this they absolutely had to take him seriously. He played the game better than they did.
In terms of his relationship to the Austrians, I don't know much from my own personal experience. I speculate that the story about the first Mont Pelerin meeting in which Friedman, Stigler and other American 'liberals' found themselves together with Mises, Hayek and a bunch of old-world gentleman, was typical of cultural dynamics that characterized the relationships more generally (just speculation). Maybe Friedman saw in Mises a stuffy, dogmatic old foreigner without much practical relevance. He represented the past and could not speak to the future in an effective way. Mises probably saw Friedman and company as brash, superficial, compromisers who were part of the problem rather than the solution.
Concerning Hayek, who later spent considerable time at Chicago, Friedman clearly owed him a great debt and was much influenced by him in his political economic writings. Friedman acknowledges this debt but is sadly dismissive of Hayek's work as an economist. I wonder still whether Friedman was really so narrowly superficial in his understanding of scientific inquiry or if this was just a strategic decision. (He shared with Hayek a fundamental distrust of convoluted mathematical and/or statistical modelling devoid of economics). Either way - not good.
I met Hayek on very few occasions and got to ask him only one question. I was a budding U of C PhD and was young and an idiot. I asked him what he thought of Friedman's monetary rule. He seemed irritated. He gave the now-familiar answer about how such a rule would never be adhered to in a real crisis (something Friedman seems to have to believe himself in the end), but then he said that, in any case, Friedman had misunderstood the role of statistics in economics and social science. I did not have the faintest idea what he meant. Now I know. At the time Hayek was in the middle of his turn to the examination of complex phenomena and he would have seen Friedman's pedestrian data-crunching as rather pathetically naive. Perhaps he was also bothered by Friedman's appropriation of the ideas of Hayek's friend and colleague Karl Popper to characterize what he (Friedman) was doing - "hypothesis refutation."
Friedman's position toward Hayek pretty much mirrored that of the rest of the mainstream profession - condescending dismissal. And the rest is history.