Bart Hickman: 300mm/F6.3 on micro 4/3 = 600mm/F12.6 on full frame or 400mm/F8.4 on APS-C. Doesn't sound so amazing to me.
The A700 (1.5x) and A900 (FF) had essentially the same pixel pitch. Using the A900 sensor and cropping instead of using film as I discussed above gives the same result. Cropping the A900 image has exactly the same gain.
There is no inherent crop factor on IS, or resolution of a crop sensor compared to FF sensor. It depends on the relative number of sensors per mm. Some systems have FF cameras with relatively low pixel count compared to their cropped cameras. The quality of each pixel might be better (larger pixel captures more photons in a given time at the same aperture), but resolution may in fact be lower on the large fewer pixel camera. For a crop camera with the same size pixels (and the same generation sensor/processing), there is no impact on noise, or DR). It does depend on the specific cameras, not a universal crop factor effect.
There is no crop factor on f/number as regards to light intensity. Take a 35mm negative. Expose it with a lens. Cut out a small section (you now have a crop sensor). Nothing changed about the light intensity in the cropped sensor.
The field of view changed, not the focal length, not light intensity/mm, or number of photons/mm.
DOF on the cropped piece of film (not the final printed image) is the same. Or if you prefer the CoC at the same distances from the focal plane are still the same.
When you enlarge the image to print or view the same size as the uncropped image the DOF on the final image will be less on the cropped image (because you have magnified the the CoC more to enlarge the image to the same size as the image from the uncropped film.)
This DOF case doesn't deal with same field of view in the cropped and uncropped images, since camera / subject distance has to be greater for the cropped image increasing DOF on the "film".