Note that the original question was between a 6k max pressure load versus an 8K pressure one in a shotgun. Both would presumably be loaded with a suitable powder & both are "SAFE" pressures.
BullsEye is "NOT" a suitable powder for loading a 150 grain bullet to a velocity of 2930 FPS in a .30-06, PERIOD! Try it & yes you will most likely Wreck your Rifle.
I believe we do need to keep our answers relative to the question being asked. Try & load a 1˝ oz load in your 12 gauge to 1300+ FPS using Red Dot or similar fast burning powder & you will also likely wreck your shotgun. That However was not the question being asked.
As to the original question which stated the Same shot load was pushed to the same velocity with one load producing 6K psi & the other 8k psi. To this point no one has stated any "Facts" which causes me to change my answer.
The difference in the strain on the action will be so small (Even though not Necessarily Exact) as to be inconsequential.
Primer flattening in a high pressure rifle load is entirely out of the scope of this question. When the primer ignites in a rifle cartridge it actually tends to shove the case forward to the extent of its head space. Pressure from the powder after it ignites pushes the case back against the breech reseating the primer. When loading low pressure cast bullet loads in rimless cases the primer thrust can set the shoulder of the case back & the pressure may not be enough to set it back. It is always advisable to keep such cases "ONLY" for further low pressure use & not to reload a full power load as it would have the same effect as excess headspace, "BUT" this is not the question we were discussing here.