I crank the ISO up and still can't get the keeper rate as high at 1/1600 and higher using f4 compared f2.8. 2.8 always wins when both have IS and the ISO is similar stops. Maybe it's more a focusing issue. I certainly came to know the intricacies of the 7D while I had it and used to kind of irritate the BIF guys with the bigger F4 lenses at times when shooting side by side, especially in the golden hour.
That's the point. Sensor size does not affect exposure. Shooting at 1/1600 s, f/2.8, ISO 3200 on APS-C, if you switch to f/4 and keep 1/1600 s and ISO 3200, you'll have half as much light per unit area hitting the sensor. Same would be true with the teeny sensor on my PowerShot S100.
What sensor size does affect is the amount of noise at a given ISO. So compared to 1/1600 s, f/2.8, ISO 3200 on the 7D, you could shoot the FF camera at 1/1600 s, f/4, ISO 6400 and have lower image noise (better IQ) or you could shoot at 1/3200 s, f/4, ISO 12800 and have similar IQ to the 7D shot at f/2.8, ISO 3200 - i.e., a faster shutter speed with the slower lens and equivalent IQ.
Here's a shot with one of one of those 'bigger f/4 lenses' at dusk on an overcast day, FF camera and ISO 6400. Same shot on a 7D would be unusably noisy (and in this case, f/2.8 isn't an option...).
EOS 1D X, EF 600mm f/4L IS II USM, 1/250 s, f/4, ISO 6400