D500 vs. D810 and rodeo photography

I am currently shooting rodeo with the D810 and a 70-200mm f/2.8 lens. My lens is not long enough so I end up heavily cropping most all of my shots. Also, the D810 does not handle noise very well. My question, if I go to the D500 (supposed to be more of a sports camera and handle noise better) and use the same 70-200mm lens and get the advantage of what will now be a 300mm lens, will the resulting image on a smaller sensor with less cropping be equal to the heavily cropped image on the D810?
thanks for your input!

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Thanks Woody but the need for heavy cropping on shots with my D810 is precisely why I am considering the D500, since with a 200mm FF lens, it effectively becomes 300mm. The article doesn't help with IQ differences using the same lens between a heavily cropped image with a full frame camera and a not-so-heavily cropped image because it is not necessary due to the added reach of a crop sensor camera. I fully get that using DX in a full frame camera is the same as cropping the image in post and that is what that article is about. Maybe I am not asking the question right.

Originally Posted by Woodyg3

It's odd that you are having problems with noise on the D810, since it is normally noted for it's low noise performance. I suspect the heavy cropping is making the noise that is present much more visible. I have certainly had this issue with my D500 and heavily cropped shots.

The link that Ivan posted is excellent, and I think it will likely provide all the info you are seeking.

Woody, that was exactly what I was looking for, thank you! I had written off the D500 because everything I read told me it was not good at high ISO. Now I see compared to cropped images on FF, and most of my images shot with the D810 for rodeo are heavily cropped, it is better. I plan on renting one for my next rodeo and testing it out. Thanks again!

Originally Posted by Woodyg3

I thought this was the link listed above. This video directly relates to your question, the D500 to D810 is about half way through the video.

https://www.youtube.com/watch?v=o6rZ4p1d56A