The problem isn't even the computer most times, its more often the display. Many modern flat panel displays have far more latency than even a crappy analog CRT, and yes the difference is definitely often noticeable if you have any experience with computers. Some of the most modern ones can be the worst offenders too, given the amount of signal processing a modern display does.
To add to earlier example, I do some retro gaming on an old windows 98 box with a CRT, the lack of latency moving the mouse in first person shooters of this era compared to today can be incredible.
That's analog for you. You essentially have a speed of light connection from the frame buffer to the electron gun, with no processing involved. As fast as the bits can be read from the data buffer they appear on the screen.
To add to earlier example, I do some retro gaming on an old windows 98 box with a CRT, the lack of latency moving the mouse in first person shooters of this era compared to today can be incredible.