The scan speed is exactly the same for all screens when driven by the same timings (resolution, blanking, refresh rate), so there is no difference there. Most digital screens have some processing lag, for gaming screens usually 1-4 ms. This doesn't exist in a CRT. LC panels have a pixel response time, somewhere around 1-40 ms depending on the color change, drive mode and panel type ("1 ms" is always a grey-to-grey transition and generally with overdrive). CRT phosphor lights up practically instantly when hit by the electron beam.

So for a given set of timings, you'd always expect the CRT to be faster, because it represents the absolute minimum time-of-flight delay, assuming it is driven by a direct RAMDAC and not by a conversion box buffering an entire frame or significant portions.

Also, you can "move" electron beams at extremely high speeds. Even in a magnetic deflection CRT like the GDM-FW900 the electron beam can move at more than 80 km/s[1]. In some electrostatic deflection systems the speed of light is exceeded: they can draw a dot moving across the face of the CRT that moves at a higher speed than c. This is possible because "the beam" is a fictional object.

[1] 2304 dots across 482 mm with a pixel clock of around 384 MHz means these 2304 dots are covered in about 6 µs; 482 mm/6 µs = 80.3 km/s.