You only pick up a hydro shield with Petra. Multiple Petra buffs don't stack, and Hu Tao acts last in your rotations so Pyro crystallize shields won't exist yet. Assuming that Xingqiu/Yelan build about 160% ER and Hu Tao builds around 200 EM, Petra buffs Xingqiu/Yelan's damage by about 18% (going from ~87% to 122%) while Instructor buffs Hu Tao's damage by around 13% (going from 200 EM to 320).

Prior to Yelan's release, Petra's buff wasn't worth it because with Xingqiu as solo Hydro, your Hydro damage is way less than your Pyro damage, and do buffing his damage a little bit was way less rotation damage. But because double Hydro makes the damage split much more even, Petra's DPS increase becomes more competitive with Instructor. And given that an Instructor build that doesn't get enough CR to reliably proc Fav also needs additional Zhongli field time to NA and proc Fav if you're E fails to do so, the field time cost is fairly similar. Petra really isn't worse than Instructor in double Hydro, it's really just a remnant of double Geo being the standard that people dismiss it.