G is a force acting upon an aircraft. It is mainly dictated by the aircraft's speed. This is why an F-15 pulling 6G can "out-turn" a missile that is pulling 20G. G-limit is simply how much stress a plane can take without breaking. The faster you go, and the more weight you have, the more stress. An empty F-15 pulling 6G is under a LOT less stress than an F-15 with 5000lbs of stuff under each wing---at the same speed and turn rate, the loaded one is experiencing more stress, and thus has a lower G-limit at that moment. (because at 6G, that 5000lbs of stuff is then inducing a 30,000lb force on each wing)
The REAL way to measure a plane's turning capability is how many degrees per second--in other words, how long to make a full circle. Of course, that is then split up into instantaneous vs sustained turn rates. Which is why aircraft have maneuvering "envelopes" composed of multiple 2D graphs trying to explain life in 3D under varying conditions.
There is no simple number/stat/answer to describe a plane's agility. Classic example is WW2. Roll vs turn. Spitfire vs Fw190. Basic Spitfire turns rapidly, rolls slowly. Fw190 is the opposite. Then they clipped the Spitfire's wings to make it roll faster to match the Fw190's roll--but that made it turn slower so it lost its turning advantage. You can't have everything.