is the hysteresys width of the schmitt trigger should be high or low and why?

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There's no single answer. Typically the hysteresis is made slightly larger than the Vpp of any expected noise in the input signal or any feedback voltage from the output to input.
 

In the vast majority of cases, it is symmetrical with respect to a trip voltage, which is to say:

Vth(+) = Vpp + delta_V
Vth(-) = Vpp - delta_V
 

It all depends on your application. To get some better feedback you may provide us more info. Generally spoken, noise or interference should not flip the status of the schmitt trigger (unless the circuit is used to detect such behavior). In feedback systems small hysteresis may lead to (too) frequent switching or an unstable system and large hysteresis may result in too high inaccuracy.
 

schmitt trigger said:
In the vast majority of cases, it is symmetrical with respect to a trip voltage, which is to say:

Vth(+) = Vpp + delta_V
Vth(-) = Vpp - delta_V
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The actual trip points Vth(+) and Vth(-) are the values of interest. Whether these are symmetrical to a theoretical calculated trip point is really of no practical importance.
 

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