So after the first “A History of Simulated Violence” mission, do I complete the “More History of Simulated Violence” mission to unlock the next OP level? If not, what is the difference between the two missions?
There actually… isn’t a difference. The only difference is that “A History…” will give you a head customization item. “More History…” always gives a random purple gun as a reward.
To unlock the next OP level, you need to exit your game, turn the OP level up as high as you can (for example, up to OP2) and then beat DP again at that level, to unlock the next one. After beating Digistruct Peak in OP2, you have OP3 as an option now when you start your game. Beating DP in OP3 mode will unlock OP4, etc.
EDIT: To clarify also, both missions will unlock the next OP level for you, even when you reset UVHM.