Trimmed sensor: Why does not the full frame have a faster shutter speed than the trim (all other things are the same)?

I enjoy amateur photography of wildlife, and I have always used crop camera bodies + long lenses, and I usually shoot with my hand. Obviously, the main difficulty is that I need very fast shutter speeds to get sharp pictures, especially of moving subjects. Equally obvious is that I have no control over the weather (also known as lighting) or wildlife. Finally, as an amateur I can not spend the amount of money needed for a main lens, for example, right now my zoom is a Sigma 150-600 Sport, f5-f6.3.

All this means that when the light is bad and / or the wildlife moves quickly, I often find myself increasing my ISO by thousands. I decided to get a full-frame camera as an alternative to change when the light is not excellent. I thought that since the whole frame collects more light, it would not need an ISO so high to obtain the same shutter speed. This would mean less noise and better shots with less light. But with some tests so far, it seems that the full frame requires similar configurations. Maybe I'm missing something?

For example, today I was taking pictures of a snowy owl. I started with my trimming camera, and with 600 mm / f8 / ISO 640 I achieved shutter speeds of approximately 1/5000. It was fine, it was sunny, but sometimes a cloud blocked the sun and the shutter speed dropped to about 1/2000, which is the minimum I like to go for subjects that could move. I decided to switch to full-frame mode and perform some tests, and found that to get the same shutter speed, I had to increase the ISO to the same configuration. Yes, the configuration of the lens and the aperture were the same, but does the full frame still not receive more light and, therefore, requires less ISO? The full frame body was firing in full mode, not trimming.

Here is the list of specific equipment, thank you very much for any advice!

  • Cultivation: Nikon D500
  • Full picture: Nikon Z 6
  • Lens: Sigma 150-600mm F5-6.3 DG OS HSM Sport

Edit: after posting this I took another look at two if the images for comparison. One difference I noticed immediately is that the full-frame image has significantly less noise, although the ISO is the same. That's great, but I still need fast shutter speeds for moving subjects. Do full frames do not require such a fast shutter speed to avoid motion blur / hand movement, etc.? In this case, maybe I could safely lower the ISO and shoot something like 1/1000?