Ser Edmund Moore is a knight at heart, he is a diligent, righteous man and rightfully deserve his place in the Kingsguard. Unlike Jon Edmund stays right by his morals and his oaths to the Kingsguard, we know that Edmund is an inspiring figure within the world but he never feels the pressure of this. Ignis's brothers Vorian and Edric admire Edmund and the Kingsguard - '“I want to be a knight and join the Kingsguard', and since Edmund is the Lord Commander of the Kingsguard he holds the responsibility of their duties, so he is much more sure about his ideas than Jon Darklyn is. Edmund cannot question his place, all the others look to him for support. Edmund is strong and firm.
He has been dispatched by the king, personally, to the Dawnlands to be his eyes and ears, so Edmund feels a sort of responsibility that everything in the Dawnlands goes in favour of Aeyron. That obviously doesn't work as Edmund fails to protect Trystane Archer and Hailee Archer, Edmund does save their son Daeron and now he feels that his duty is to protect Daeron and perhaps raise him now -- as a consequence of his failure to save his parents.
Edmund feels immense guilt towards Daeron, and their time stuck in Oflus doesn't help him. Knowing if they were stranded there forever, it would be easier for Edmund to survive. For once, his morals are being questioned by this accursed world, however he reaches deep within himself and does what he does best - be a knight. So he teaches Daeron swordsmanship, taking the child as his own apprentice, he knows that taking care of Daeron is the best thing he can do after his failure at the Dawnlands. 'It’s all my fault. Aeyron had sent me to the Dawnlands as a representative for him but I had failed my duty to Aeyron to protect the Dawnlands and all its people'.
Edmund resumes his status as Lord Commander during The Battle of the Bloodwater, when Aeyron goes missing he assumes his natural hierarchy over the Kingsguard and orders them to find him, even arguing with the now-confused knight Ser Jon Darklyn. The guilt is put behind him for now, as he doesn't let the pressure get to him as Lord Commander.
As a whole Edmund remains still as a wall in book one. He doesn't question his faith or his humanity, but he does have lingering guilt for failing his job in the Dawnlands