While the static access is acceptable (to an extent), with the dynamic approach you can pass the object transitively to the 3rd side object via dependency, (otherwise also the transitive call the transition of dependency would have to be initiated from the original class), which needs not to be pushed some data, but rather the dependency decides and pulls the data/method it needs be it multiple times in a single method. Otherwise way it can only return, while instance can be called, not-separated wrapper method logic from data. Instance inline code seems to be shorter, and when you remove an instance, all their calls complain at that moment, whereas static class continues to preserve unnoticed in the code as they don't need the instantiation prerequisite.
Static classes preserve their state in between various objects, and methods contexts and thus are not automatically "reset" as it is with the 'new construct'. Instances encourage more transparent pure functions approach - passing parameters. When you pass an object, you don't separate the service logic from it's data structure, when you pass only the array data structure, the execution logic is lost in transit or separated into another place and must be eventually called intransparently statically when not-passed - pure functions concept.
I would use comparison with Einsteins vs Newton's equations. In some cases, they look totally the same. But to be pretty content I would use more versatile instances or service locator singletons, vs static classes. On the other side, the less "versatile" static classes might be initially easier to implement, especially if you don't plan on rocket with them as far as to the space orbit as you might get with instances. Similarly as with private attributes you signal they are not passed anywhere, pure functions, though it might less often signalize also the bad, being called from anywhere.
