I can't find whether or not Canon's Mode 2 will follow vertical pans but this says Sigma's isn't designed to do that.
" But do also note: In order to give the appearance of stillness/sharpness to an object moving parallel to the capture sensor, the camera and lens must move at a pace that matches the speed of the object moving through the frame. This is called “panning.” And some of our larger OS lenses offer not only ON and OFF for OS, but OFF/ 1 & 2. On Sigma lenses with Off/1/ 2 controls, OS 1 corrects for any lens movements, while OS 2 only corrects for vertical shakes–meaning you can follow and pan fast-moving objects with or without a tripod, and the OS won’t correct for the chasing of the subject along the horizontal axis."
That was copied from this article.
It's a bit harder to interpret Nikon's explanation here.
"For a panning shot in which subject movement needs to be emphasized, in the case of a subject moving horizontally, if horizontal blur is corrected by the VR function, the panning would be insufficient to achieve the desired effect. To counter this, Nikon's VR (Vibration Reduction) detects camera movement for panning, automatically suppresses the blur-correction function, and reduces blur in the vertical direction rather than the camera's direction of movement. With this function, the panning effect is maximized. Panning Detection is effective regardless of the camera's orientation or direction of motion."
Which was copied from this article.