I first saw the POB in the mid seventies. The dancers were technically very strong, but the problem seemed to be that there was a lack of discipline, no strong direction and (perhaps) the general administrator wasn't that interested in dance. Also, there were a great many restrictive practices which made it a very difficult place to work. So the company atrtacted little attention outside France. This changed to some extent when Rolf Lieberman took over direction of the theatre. He was interested in both opera and ballet and was a good friend of Balanchine (Chaconne has its origins in dances which Mr B did for a production of Orpheus given in Hamburg when Lieberman was director there). So a great deal of Balanchine was added to the rep, including several pieces from the Stravinsky Festival which Balanchine rehearsed himself. Likewise a number of ballets from the Ravel Festival came into the rep (Lieberman helped with negotiations with the Ravel Estate I believe). It was also during the Lieberman era that Cunningham created Un Jour ou Deux for the company. A really interesting piece and the dancers were wonderful.
Verdy had two difficult years, but did bring MacMillan's Song of the Earth into the repertory. Then came Hightower, who among other things managed to increase the number of performances and I actually heard her say "I'll keep them so busy they won't have time to plot". Things were a great deal less str5essful for the direction (there was one strike and a postponed premiere but that was because the stage was infested with bugs because of real straw bales used as part of the decor for Heinz Spoerli's Fille Mal Gardee). Then in 1983 came Nureyev who found a galaxy of talent at all levels. Claude Bessy took over the direction of the school in 1973 so dancers like Piollet, Pontois, Loudieres, Thesmar, Bonnefous, Guizerix, Denard and Jude, at the top of the company when he took over, were all products of the old school - and wonderful dancers they were. (Platel actually trained at the Paris Conservatoire).
My impression is that Nureyev didn't try to influence style but always gave opportunities to young dancers (often despite custom and tradition) and opened up the repertory still more trying to stretch both technique and interpretation. (There's a story about him at the Royal Ballet working furiously to master a sequence of steps. Michael Somes saw him and said "It would be easier and would give the same effect if you did ............................" To which came the reply "How will I improve if I don't set myself something to do that I can't do".
It's a long time since I saw POB so I don't know what the company is like now - I've heard ominous reports, But I have no personal knowledge.
As to the Royal Ballet, they have some wonderful dancers but the Ashton style "What used to be known as the English style is in fact the Ashton style" as someone wrote, really went when MacMillan took over. The level of the men was with a few exceptions pretty weak, and he was heard to complain that the company danced Petipa like they danced Ashton.