Aircraft pulling the same G in level flight will have the same rate of turn.
If a Tucano, Tornado, Typhoon and F15 all pull 4 G in level flight, they will turn at the same rate. In other words their noses will move through the same points of the compass at the same time. Neither will be able to get their nose onto the other if they stay at the same G in level flight. The speed, angle of bank and radius of turn and power they each need to achieve this level of G will differ according to their wing loading and other aerodynamic factors, but whilst pulling the same G neither will be able to out-turn the other in level flight.
Agree with your first bit, but the bit quoted above is wrong.
First of all, bank angle is directly related to G. A balanced 60 degree banked turn in level flight will result in 2g, it must, just have a look at the old lift vector diagrams. At 60 degrees, the lift vector must be twice as big as the weight vector to give a vertical component of lift equal to the weight vector. G is directly related to the relative size of the lift vector.
To illustrate how it is wrong, you need to go to some extremes, this is where my tiger moth traveling at 85 mph and your Foxbat travelling at Mach 3 help out.
My tiger moth, in a 60 degree banked turn will pull 2 gs and whip around through 360 degrees in under a minute. Your Foxbat, travelling at Mach 3 will take a long long time to do 360 degrees in a 2 g turn.
Another illustration. A rate one turn which is defined as being 360 degrees in two minutes, requires a higher angle of bank, and therefore higher g, the faster you are going. In a light twin, a rate one turn is generally less than 25 degrees bank, in a faster passenger jet, the rate one turn requires more angle of bank, to the point where passenger jets are limited by 25 degrees bank angle during instrument procedures and light twins are limited by rate one. The only reason for this is that the passenger jet is going faster, if it slowed down to the speed of the light twin, the rate would be the same.
So. An aircraft travelling at the SAME SPEED and pulling the SAME G and therefore at the SAME BANK ANGLE, will have the SAME RATE and SAME RADIUS. Doesn't matter if it is a Tiger Moth or a Foxbat.
Lets look at extremes again to see why an aircraft with a low wing loading can out turn an aircraft with a high wing loading. Lets say the low wing loading aircraft is the Tiger Moth and the high wing loading aircraft is an experimental aircraft very similar to the Tiger Moth except it has such stubby wings that at 85 mph it requires an angle of attack close to the stalling angle to generate enough lift to maintain height.
Both aircraft cruising along at 85 mph together and they both enter a gentle 15 degree bank to the right. Both aircraft increase angle of attack slightly to maintain altitude. This brings the experimental aircraft even closer to the stalling AoA but at the moment it's not quite stalling.
Both aircraft are now at the same speed, pulling the same G and getting the same rate and radius of turn.
But what happens when the Tiger Moth increase bank angle even further? The experimental with very high wing loading tries to match it but doesn't have any excess angle of attack to use and stalls. Meanwhile the Tiger happily putts around in a nice tight turn.
So while the Gs and speed were the same, the aircraft had the same turning performance. But the low wing loading on the Tiger Moth meant it had plenty of excess angle of attack to use to further increase bank and therefore rate, radius and G.