Static is a singleton. singleton instance with non-static methods need only when you need multiple Utility class variations with different property(ies)/setting(s) value(s) to use. As example when your utility has some property (i.e. customProperty) and you need two different cases at the same time.
when Utility need to use customProperty=value1
when Utitlity need to use customProperty=value2...
but it is quite strange, clumsy and not good... Utility caller can provide needed property value into static method.
So, do not stuck with that. Make Utility methods always static and do not care about "theoretical" patterns... :)
