It is worth pointing out that both programs have expiry of points, whilst Amex, as far as I know, doesn't. So unless you are planning to close down your Amex card, it is worth waiting until you are (almost) ready to use your points before you transfer them. In fact Enrich (used to) allow you to hold an award ticket for a few days whilst the points were transferred from an external program, not sure if they still allow this, but I know Krisflyer doesn't.