Yes, the basic "exposure setting" will be the same at any given f/stop and ISO. But the image quality isn't; you have to turn the ISO down 2 stops on the micro 4/3 camera to achieve the same image quality.
I never said the LENS is 2 stops better, I said the larger SENSOR (or rather, the whole camera) has a two stop speed advantage. And one of the reasons is that a full size lens' circle of light covers 4x more area than a micro 4/3 lens does, delivering 4x the number of photos (light information) to the sensor at the SAME exposure. Therefore the lens does play a part in it.
This can be quantified as the amount of GAIN (signal amplification) that the system needs to output to deliver the same level of final image brightness.
On a micro 4/3 sensor, the signal gain (signal to noise ratio, and thus the image quality) at 100 ISO is the same as the signal gain at 400 ISO on a FF sensor.
400 ISO has the same signal to noise ratio as 1600 on FF, and 800 the same as 3200.
A sensor is a photon collector; a full frame sensor collects 4 times as many photons (signal) at the same exposure reading as a micro 4/3 sensor does, while the background noise remains constant.
4x the signal = 4x signal to noise ratio at any given ISO setting.
So to achieve the same image quality, you have to set the ISOs differently as described above, and stop the lens down 2 stops on the FF camera. Now both sensors are collecting the same number of photons which = same image quality, and not so coincidentally, the depth of field becomes the same too.
The following settings will give virtually identical results in terms of:
1. Field of view, 2. Depth of Field, 3. Motion Blur, and 4. Image Quality (Noise/Graininess)
25mm lens, f/2, 1/60 second, ISO 100
50mm lens, f/4, 1/60 second, ISO 400
You will notice that the aperture diameter (focal length divided by f-stop) is the same in both those scenarios: 12.5mm. That's one of the reasons they're equivalent. A full size 50mm f/2.8 lens is equivalent to a M4/3 25mm f/1.4 lens, once you equalize the ISOs to the same signal-to-noise ratio.
The lens isn't "faster", the whole camera is. Everyone already knows FF cameras deliver better low light performance at the same settings; they're faster. The whole system is about 2 stops faster overall, so you can just bump the ISO up by 2 stops and get the same results.
In the example above if you wanted to shoot faster, you could do it with the FF camera by keeping the ISO at 400 and setting the lens at f/2. Now you can shoot at 1/120 second--that's two stops faster with the same image quality. To achieve the same 1/120 second speed on the micro 4/3 camera and maintain the same image quality, you would have to set the f-stop to f/1.0. But you can't because the lens isn't that fast.