The Cairns RWY 15 EOI procedure, as designed by myself and others, in this case, is identical to the SID. It has to be due to terrain considerations. The difference is that the OEI procedure is predicated upon a 15° bank angle, not 25°. A sped limit, for the AEO SID, and the OEI Special Procedure is essential to 'contain' the turn radius.
A fairly rare case where the OEI Special Procedure and the SID are the same or very similar.
Regards,
Old Smokey