Don’t overcomplicate things by bringing in power or thrust. Let’s stick to the original question.
Aircraft flying at the same speed using the same angle of bank will have the same radius of turn.
Example 1: The Battle of Britain Memorial Flight. A big Lancaster with a Spitfire and Hurricane in perfect formation (as always) on each wing. Lanc puts on 25 degrees of bank, Spit and Hurricane put on 25 degrees of bank. Result? They all go around the corner together in perfect formation.
Example 2: Air-to-air refuelling. Tristar tanker trailing hoses with an F3 Tornado hooked up and a pair of Harriers in close formation on the Tristar’s wing waiting for their turn. Tristar turns using 20 degrees of bank, Tornado banks likewise to stay hooked up, and so do the Harriers. All turn neatly together.
That’s the speed, angle of bank and radius bit sorted. Different wings, different weights, but at the same speed and angle of bank, they all stick together.
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.
This is why in air combat you have to learn about using the vertical, ie to get out of level flight and use earth’s gravity to increase your actual G relative to your opponent (the “combat egg”, high and low yo-yos etc) and the principles of lag pursuit and lead pursuit which accounts for different wing loading in dissimilar air-to-air combat.
Google the above and no doubt someone, somewhere, will give you the mathematical formulae in a format you can understand. I've given you the real world examples.