The surrendering bandit fired an arrow at the mc and only surrendered after the other archer got her neck broken. Surely glenval has a jail and the mc has rope just like the second situation
You both make a valid point. I'd wager maybe the MC might have wanted to prove he's capable of killing bandits (Glenval bandit) as Athagan later disclosed to place MC in situation where killing is justified and commonly accepted, whereas the 2nd bandit encouter gives the MC the option to follow procedure of trial if the possibility is given.Yes, MC has the authority to kill the bandits while doing the patrol mission, but there's big difference in killing an bandit that throws their weapon down and surrenders to killing bandit that is fighting to the last. Even if the bandit originally attacked the MC's party.
To respond in your modern perspective: Even if criminal has shot at the police officers, they still can't execute the criminal if the criminal throws their weapon to the ground and informs that they surrender. In that situation the law requires police to capture the criminal alive, sure in some places around the world the cops might get some leniancy for still killing the criminal, but in the eyes of the law they should arrest them when they clearly have indicated surrender by throwing their weapon on the ground and raising their hands above their heads.
I myself spared the bandit and Athagan did take a positive note on this decision. It would follow suit of refraining from harming the elf princess hibernating on the road according the thought of not making grave decisions while agitated.