The way the staggers work is (from memory)
3/5 Yellow !! and simple stun with a lower chance to trigger. Ups chance to drop stuff.
4/5 Blue !! terrors, and once again ups trigger rate\drops.
5/5 Red !! Terrors, wipes 2hr if used (useful on plds) and locks it and prevents it from being used if it hasn't. Can trigger even more (but can still be a PITA as it can take me upwards of 16 attempts) and has highest drop rates. Tends to give 1 peice of currancy per staggered mob with no TA with a max of 4 with TH. Also impacts general mob drops like NMs dropping the zone boss pop.
My ancidotal evidence says 5/5 rains AF like candy (20-30 peices per run. Blu seems the rarest) and is the only way to get the exceedingly rare 100 peices.
Mages are staggered by magic, then the rest are JA or WS based on their jobs.
Edit: There's no specific magic or JA that stagger, it appears to be based on what you bring in.