Between the two, I'd normally consider Castrum slightly more favorable if you're a tank or healer used to 23-25 minutes dungeon runs (those 23-25 minutes includes the unskippable cutscenes.) But the queue time can be a hugely variable factor/wild card at different times of day for Hidden Gorge. [The latter may be faster if more people are willing to queue for PVP.]

For me personally, I'd run Aurum Vale with my full Offensive 5 squadron when I'm healer to clear the dungeon in less than 15 minutes for 5 Moogle tomes. [I already gotten the Kojin and Ananta Beast Tribe quest area themes in 3 completed runs. I spent only 14 Moogle tomes total. In addition, I am currently lower ranked for both beast tribes at the moment, so the Moogle tome event gave me an easy alternative to earn and use the orchestrion rolls.]

At the end of the day, your mileage may vary.