That's a good question. From the "birder" point of view, I think it's the pixel density that is paramount, rather than the "crop factor". My M6 II can put a lot more pixels on a Blue Jay than my 5D4 can at equal distance with the same lens, but the 5D4 does a better job with high-ISO. And if that Blue Jay is in the deep shadows of the woods, then it's the 5D4 that wins that battle. However, the ISO difference isn't but a stop to a stop and a half, so just getting an extra stop through the lens by NOT using a teleconverter helps a great deal.
I did some side-by-side between the M6 II and 5D4, with the 1.4X added on the 5D4 shots vs. the bare 500/4 lens on the M6 II. Fairly comparable in terms of noise, though I didn't get too extreme with the ISO. I'd say that it still slightly favors the 5D4, but the ability to avoid needing the 1.4X is something to think about too.
Can't say a lot about the tracking of the little M6 II, as I haven't has much experience with that aspect of its operation yet.
Getting that kind of pixel density doesn't require a crop sensor, though getting enough speed to handle uncropped 4K may be a different story. But that's a different subject.