The term CB-IR is a term used to describe the training route towards an EASA IR(A) and not a qualification itself. The qualification is the same EASA IR(A).
There is a difference between an IR(A) gained via the competence based route and the integrated route and that is it does not permit the exercising of the privileges in a high powered aircraft (HPA) because the Learning Objectives (LOs) are not included in the CB-IR Theoretical Knowledge (TK) course and exams.
It would be the same if you trained for IR in a single engined aircraft you cannot exercise priviledges in a multi-engined aircraft but the underlying IR(A) is still the same EASA IR.
That said though there is nothing stopping a pilot completing their ATPL exams and flight training using the CB-IR training route and being able to exercise the IR(A) privileges in an HPA.