Compare superzoom image with DSLR image

I have the Nikon P900 with its 2000 mm effective focal length generated by a 357.5 mm f/6.5 lens on a 1/2.33" sensor. I use it handheld mostly for birds, trying to get shots good enough for ID on iNaturalist. I have tried a Canon 7D with the 100-400 lens for comparison, which works out to a 640 mm effective focal length. I prefer the Nikon for exactly the reasons you are asking about. That said, the images often do not have the "snap" you can get from a nice DSLR photo if you are close enough. Getting close enough can be hard work. The other downsides to the Nikon are that it is probably slower to focus and does not have a usable manual focus. If you have a bird with some branches in front the camera will often focus on the branches. Spot focusing will sometimes let you focus correctly, and sometimes you will get lucky. But nothing competes with the reach. The lenses are not too different in focal length or f/stop. I want a zoom sensor behind the lens, so I can use big pixels when I am close.

I did a direct comparison between a Canon 7D Mk I with the 100-400 zoom (first generation) and the P900 in a range of distances in good sunlight. Roughly, I preferred the Canon when the "right" effective focal length (so the bird fills the frame) was about 1200mm or less. That results in a crop to about 1/2 of the frame in each direction. The better lens and lower noise overcame the fewer pixels on target. When the "right" focal length was longer, the pixels on target from the Nikon won out because the crop of the Canon was more severe. The further from 1200mm, the clearer the difference was.

This is not a simple question to answer as there are many variables; but the simple answer is that the probability of recording a better image exists with the APS camera.

With the SX50 you have a 5.6x crop of a 215mm lens' image circle. And with the APS you have a 4x crop of a 300mm lens' image circle; which means the APS retains more of the light from the scene/image... advantage to the APS.

At 215mm the SX50 lens is at f/6.3 and projects details at a minimum average size of approx. 9microns, which is approximately 6x the size of a pixel on that sensor (1.5um)... but that's only if the lens were optically perfect, and that lens most certainly is not. Best case (theoretical) scenario is ~ .35MP average of recorded resolution w/ a lower contrast level... reality is probably notably worse.

With the APS there is the potential of using a faster and better lens, lets say a 300/2.8. At f/2.8 a lens projects details at an average minimum size of 3.8 microns. Or say a 300/4 which will project details at an average minimum size of 5.4 microns. Both would fit within the size of a pixel of most APS cameras (or w/in the diffraction limit of 2x). E.g. the D7500 has 4.2 micron pixels and ~ 8 micron diffraction limit. Best case (theoretical) scenario, ~ 2.5MP recorded resolution with a much higher level of contrast... advantage to the APS again.

Edit: even the 70-300vr would be at f/5.6-300mm and could project details at an average minimum of 7.5 microns, less that the D7500 diffraction limit (again theoretical, the lens probably isn't that good wide open).

Then there is the consideration of motion (camera shake/subject/atmospheric/etc)... and again, the larger pixel size on the larger APS sensor gives a potential increase in actual recorded resolution because a detail can move much farther before crossing an equivalent number of pixels.

For a comparison you should first compare the field of view the different setups provide. You can do this by looking at the full-frame equivalent focal length of the lenses:

Canon SX50: According to the specs provided by Canon (https://www.usa.canon.com/internet/portal/us/home/support/details/cameras/point-and-shoot-digital-cameras/long-zoom-cameras/powershot-sx50-hs/powershot-sx50-hs?tab=technicalspecifications) it provides a maximum full-frame equivalent focal length of 1200mm (that is 215mm physical with a crop factor of 5.6).

Nikon D7500 with 300mm: Nikon DX cameras have a crop factor of 1.5, resulting in a full-frame equivalent focal length of 450mm.

Now you see a factor of 2.7 between these focal length. Cropping the image of the DSLR to the field of view of the Canon SX50 would result in a resolution that is only (1/2.7)² of the original image, for the Nikon D7500 this would result in only 20.9*(1/2.7)² = 2.5MP.

Even considering improved SNR because of the newer sensor with bigger photosites the quality is probably worse compared to the full 12.1MP image of the SX50.

If you would instead use a 600mm lens the DSLR would certainly win: This would come out to a field of view that is wider by a factor of 1.3, which in turn means cropping to equal field of view results in 11.8MP. Obviously the 600mm is significantly heavier and more expensive.

We can not answer that over the internet.

Seems like you need to get a DSLR and a 300mm lens and Do a test shoot.

Find a stationary subject set up your tripod and do a test shoot with both cameras. I.E.carry out your hypothetical situation you described.

How do you compute this?

That is up to you and your criteria, compare the images with your eyes and on your computer to see how they differ.

Of coarse those test results will only apply to the two specific camera/lens combos in that test.