Differences between the Morrow and Smith-Watson Topper corrections:
In the Morrow correction, the influence of the main stress value is only considered for the plastic behaviour.
In S-W-T the influence is considered for both, the elastic and the plastic behaviour, this is the reason why it is regarded as a little bit more conservative.
As a general rule, Morrow´s correction is more suitable to use because it takes into account the main stress when the stress is a result of compression. In this case, S-W-T produces a singularity in the equation.