What is dead band width? Many servos have dead band width of 1 to 2 micro second while others have 10 micro seconds. Which is better and why?

The servo is controlled by a string of pulses, normally 60 pulses per second. The pulse width controls the servo position, 1 msec for full right and 2 msec for full left. If the pulse width is 1.5 msec the servo is centered. However what happens if the pulse changes to 1.5 msec+ 1 usec. If the dead time is 2 usec nothing happens. If the dead time is zero the servo will do a constant dance.
I have no idea what is best, whatever works.

You can say dead band width is a way to say how accurate the servo try to hold the exsact center position. As a stand alone servo small DBW is best to use. But if you run more than one servo per rudder surface one servo is usually set to minimum DMW and then you reduce DBW on the other(s) allowing for less binding because the mechanical setup is hard to get perfect. This reduce stress on servoes and current consumption.