From what we have found, Private Annuity Plans available in the market tend to supplement CPF LIFE instead of replacing the CPF LIFE.
Instead, Private Annuity Plans can be used together with CPF LIFE to
1) Boost your monthly retirement income.
2) Help you withdraw out a portion or the whole of your Retirement Sum.
1) Potentially higher returns (Annuity plans invest your money into a unit trust which can bring high potential returns. However, this depends a lot on the trusts that the insurance company invests in).
2) May comes with rider benefits (Eg; cheaper insurance premiums if you buy other INSURANCE from the same insurance company you bought your annuity plan).
It is fairly difficult to plan for your Private Annuity Plan to replace your CPF