You can understand why John Wayne disliked Clint Eastwood’s movies. Both were/are conservative, macho men, who usually played lone wolves. Wayne usually played heroes who fought the bad guys honestly and cleanly. Eastwood was an antihero, whose Westerns and detective movies showed moral ambiguity and flawed heroes. The society that you saw in Wayne movies was fundamentally sound, with bad guys like Liberty Valance being outside decent circles. There was also a funny sidekick to Wayne like Andy Devine or Walter Brennan. In the Eastwood movies, the society in San Francisco or Lago was as corrupt as the villains and the Eastwood character was at war with the corrupt officials as much as with the bad guys. There is far less humor in Eastwood movies, with his partners often getting killed like in the Dirty Harry movies or The Outlaw Josey Wales.
Eastood movies are more true to life.