Bayer sensors use a Color Filter Array to capture RGB data - either Bayer or X-Trans.
That is - the raw sensor just counts how many photons reach it, but to capture full RGB color data, it puts a filter for either Red or Green or Blue above a given photo site.
Foveon (Sigma) sensors do not. They use how deeply light penetrates into a piece of silicon - "Red" wavelengths being longer than "blue" - depth can be used to extrapolate color data.
When it comes to Black & White images.
Foveon sensors are counting "all" of the photons at every photo site giving them great monochrome rendering.
Monochrome sensors (sensors without a color filter array - either the Leica Monochrom or a
MaxMax converted camera) will simply count the number of photons that reach any given photo site - also giving them great monochrome rendering.
But they cannot capture color.
Foveon sensors count - red or green or blue - data at every given photosite. (or something analogous to this).
Though they suffer from other issues - such as not being as good at high ISO values.
I would rate cameras in this order for monochrome ability.
In good light - low ISO without a ton of dyanamic range
Foveon > Monochrome > X-Trans > Bayer
In low light - high ISO or with high dynamic range.
Monochrome > X-Trans > Bayer > Foveon
With Bayer edging out Foveon for being able to shoot just fine at ISO 6400.
But yes - without a doubt, under good circumstances, Foveon (Sigma) sensors do much better than Bayer sensors.
If my main goal was black and white photography I would choose either Foveon or a Monochrome sensor every time and ignore Bayer or X-Trans sensors entirely.
But - since I also shoot color, I must pay attention to all four.