A CA can do ICWA since he will not find it difficult. But a Cost Accountant will not do CA as he is content with what he has. The ICAI has been formed by an act of Parliment, hence the existence of the ICAI is unquestionable by any body in India. If you find the qualified guys, a Chartered Accountant is more knowledgeble than a Cost Accountant.
Finally, to have a conclusive and informed opinion, you please visit the C.A. Exam Center and Cost Accountants' exam center, just half an hour before the exam starts. Really you can find the pin drop silence at the C.A. Exam center when hundreds of examinees have assembled out side the exam hall. In contrast at the I.C.W.A. exam center you can find a noise condition all along till all the students enter the exam hall.
Because majority of C.A. students are serious and majority of I.C.W.A.students are casual about their exam. This I've practically seen.