There are different type of maneuverability. The most versatile and effective type of maneuverability in air combat is energy maneuverability. Energy maneuverability requires the ability to in moving to and from combat, and having high thrust to weight ratio in combat. This in turn puts a premium on engine performance.
Here china has been and remains behind.
In the 1950s, Chinese favored agility with its fleet of mig 15, 17 and 19 in confrontations with American pilots in Korea and with American trained pilots over Taiwan strait. Agility is different from maneuverability. Agility is the ability of an aircraft to rapidly change its heading. Maneuverability is the ability of an aircraft to rapidly move between different altitudes and locations in the battlefield. And agile aircraft might turn in a very small circle. And maneuverable aircraft might turn in a big circle, but it can complete the circle in less time than an agile aircraft. And agile aircraft might break left and then break right in a split second. And maneuverable aircraft might not go from the one to the other as quickly, but can cover more distance to the left or right more quickly once it has braked. An agile aircraft might pull out of dive and enter a climb very quickly. But an maneuverable aircraft can gain or lose altitude much more quickly.
By the late 1960s, fighter designers have done comprehensive studies of all the air-air combat victories ever recorded. They came to a startling conclusion, which is between two situationally aware pilots maneuverability trumps agility every time. An skilled and alert pilot in an agile aircraft can only some times avoid getting shot down, but always has little chance of shooting down a skilled and alert pilot in an maneuverable aircraft. A skilled pilot in an maneuverable aircraft on the other hand, can usually shoot down a skilled pilot in a agile aircraft. Furthermore a pilot in a maneuverable aircraft is much more likely to catch a pilot in a agile aircraft unaware than the other way around. Being caught unaware by the opponent who is gunning for you turned out to be responsible for more than half of all losses in combat between fighters.
So all fighters designed since 1970s has emphasized maneuverability over agility of the sort the Chinese PLAAF had believed to be critical during air battles over Taiwan straits in the 1950s.
I wonder if agility makes a comeback if stealth makes getting a lock hard. Certainly it would matter more in a gun fight than an exchange of missiles.
I also wonder if improved missiles makes maneuverability less important than agility. You may not be able to out turn modern missiles but you may be able shake then with a quick roll or some very quick instantaneous turn.