Suppose you have to invest either in secured debentures or in unsecured debentures. In what type of debentures will be prefer to invest and why?

The answer given by Hanna is correct. Given a choice, it would be preferable to invest in secured debentures rather than unsecured debentures if all other deciding factors are same in both types of debentures. This is because secured debentures are backed by a specific asset of the company and hence, are more secured or certain in repayments of their principal amounts.