Hi,
IMHO you can't say "a priori" which criteria you should follow, because any criteria encomprises "safe" stress states that are good for some applications and bad for others. In other terms, depending on the stres state a criteria can be over- or under-conservative. The best example is if you compare VonMises with Trescà-Guest, as it has been pointed out by Feajob.
In the USA the stress intensity is commonly used (SINT in Ansys), while in Europe the convention is to use VonMises (SEQV in Ansys), as you can see if you compare ASME norms to EN. ASME are known to be extremely conservative overall (i.e., on the other hand, extremely safe) because they use both conservative criteria (Trescà-Guest "everywhere"!) and conservative limits.
Just my two-pence thoughts...
Regards