Nope. It an experimental measurement that DOES depend on the interpretation chosen. If (otherwise QM-compatible) local realistic theories (a.k.a. local hidden-variables) are true, abs(delta)=2. If standard QM (without hidden variables) is true, delta=2*sqr(2), and the Bell inequality is violated (as was shown to be the case).
What differs, in a nutshell, is the ontology pressuposed by the theory in each interpretation -- once a component associated with "strictly philosophical" discussions, nowadays proved to have measurable experimental consequences. Thus the term "experimental metaphysics" coined by philosophers of physics Abner Shimony and Michael Redhead.
The outermost formalism is in both cases the same, but it is a narrow view to think that formalism is all there is to theory. It is but an element of it. Theories include, in a substantive way, e.g. ontological commitments and methodological assumptions as well (to speak nothing of values, etc).