Hard to get good stats from a thread like this where people will tend to post if they have really bad RNG experiences. From my own experience, I think the drop rate is about 20% or thereabouts.

Frankly, I feel this is one of the best designed of the relic quests (the best was the first one - prove your mettle in difficult dungeons). The dungeon spamming provided the soldiery needed and gear drops for GC turn-in to get the bombard cores. Likely most people that play this game enough to even be on the zodiac quest will not have trouble getting the gil for the other items and it provided some much needed business for high level crafters.

Atma weapons were a nightmare of very low drop rates, Animus was a long grind and the FATE component was very painful (who wants to sit and do nothing for hours waiting for a FATE to pop), Novus was a ridiculous grind and extremely expensive for the materia, Nexus was the most frustrating grind fest with very little feedback on progress.