The Arisen and Priden racial are for different uses in my opinion.
Situation (Arisen): Your tank is at 5% HP and you have no fanaticism. You use your racial and gain 20% bonus healing effects, but have no fana, you start dedicated plea and hope it hits before your tank takes the final blow. Unfortunately, it failed. Your tank died.
Situation (Priden): Your tank is at 5% HP and you have no fanaticism. You use your racial and gain 4 fanaticism stacks. You cast 4 holy healings very quickly. Your tank is now at 40-100% hp and your party/raid did not wipe.
The above situations show how the Priden racial can be the most beneficial in certain situations.
The below situations will show how the Arisen racial can be the most beneficial in certain situations.
- - - Back when we used to need to run 2 full healers in astral parties in order to succeed - - -
Situation (Arisen): Your tank is at 30% HP, your 2nd healer just died, the boss is still at 25% hp. You have to pick up some slack for your fallen healer partner. You activate your 20% bonus heals for 20s. This allows just enough to keep your tank above 1% hp for long enough for your DPS to take down the mob.
Situation (Priden): Your tank is at 30% HP, your 2nd healer just died, the boss is still at 25% hp. You have to pick up some slack for your fallen healer partner. You activate your 4 fanaticism stacks from your racial. You blow through them in a matter of seconds and manage to get your tank back up to 50% HP. The fight lasts longer than you expected and you can just not do enough healing for 2 people with only a 4 fanaticism stack bonus. Your tank dies and your party/raid wipes.
So, as you can see, they are used in different situations. That being said, when you get the Book of Ancestral Secrets, you get all the racials and you should put all (well maybe not all, but for sure Arisen/Priden) on your bar so that you can activate whichever one is needed at the exact time you need it.
Good luck and happy healing!