Received my Tamron 17-70mm today...

ZapperVT wrote:

The important parameter for image quality is the TOTAL light gathered: i.e. the light intensity on the sensor times the size of the sensor.

The f/2.8 produces twice the light intensity on the APS-C sensor, but the sensor has half the area compared to the full frame camera. So the total light (light intensity times the sensor area) is the same as on the full frame sensor which has half the light intensity but twice the area. Hence the image quality is also the same.

Fuji APS-C
23.5x15.6mm = 366.6 sq mm

Standard Full frame
36x24mm = 864 sq mm

Ratio:
366.6 / 864 = 0.4243
864 / 366.6 = 2.3568

F numbers refer to size of aperture and do not necessarily indicate illumination.  The better number to use is the T number, but these T numbers are hard to find with a lot of lenses except cine lenses.  Generally, the more elements a lens has, the greater will be the deviation between the T number and the F number.  I've found Fuji lenses such as the 50mm F2 WR to be dim, compared to low cost (and simpler) manual x-mount primes.

If we go with T numbers, T2.8 delivers twice the light intensity (photons per square millimeter) compared to T4.0.  I'm not sure about this but it seems to me to make sense.

If T4.0 is taken as reference intensity of 1.0, then T2.8 would be intensity = 2.0, if all other aspects are equal (scene, and scene illumination etc).

For full frame (light intensity x sensor area) we would have 1.0 x 864 = 864

For Fuji APS-C we would have 2.0 x 366.6 = 733,2

So, Full Frame is 864/733.2 = 18% better than APS-C in this comparison.

Is this visibly better?  Maybe.