If I read between the lines correctly, both the old and the new fan have only 2 wires, and the circuit supplies a PWM waveform to these two wires, with an increased duty cycle to get higher speed.
If the above assumptions are correct, then the old fan was brushed, and the new one in brushless.
Brushless DC motors are not intended to be powered by a PWM signal, as you keep turning on and off the supply to the electronic controller inside the fan!
If you ignore this, they will buzz and be unhappy, and the controller may fail prematurely.
Brushless fans that can accept a PWM signal for speed control usually have 4 wires: GND, +VDC (constant voltage!), Tachometer out, PWM signal in.