The main advantage is that it makes your design intent clearer, and enforces those intents. For instance you cannot inherit from a static class (i.e. specialize it), and you cannot make an instance of it (it is in effect a singleton). These would both be design intents of your utilities class.
However, static classes and methods should be used with caution, as it makes it difficult to vary behaviour of your program. Static classes and methods are very concrete and cannot be (easily) substituted, as would be the case if you used interfaces and constructor injection. Static classes and members can however be useful, but rarely. Overuse of statics make your software less flexible, and more difficult to test.