The absent Captains always appointed a deputy for while they were ‘away’. A lot of them had bought their Captaincy and/or were connected at Court. I’m quite sure Mountjoy would have had them hanged if he could have got away with it. He was a brave man in his personal conduct and expected the same in others.
The English used slightly/many more calivers than muskets depending. As you say muskets had greater armour piercing ability but they were heavier and more cumbersome to load and fire hence the support. So the troops carrying them moved slower and the rate of fire was lower.
The Irish were as you say.
The other key differences were that English shot had pay deducted for every shot they fired and so never practiced. Compared to the Irish shot they were also under officered-5 to a Company compared to the Irish 8. The English troops were mainly unwilling conscripts volunteered for service by their social superiors at home. Naturally, they resented it.
The Irish shot were all volunteers who signed up for pay and were supplied with munitions and weapons at their officers expense. They were encouraged to perfect aimed fire. By becoming soldiers they improved their social standing and gained a new income stream accordingly they were well motivated.
I think in terms of the Irish War the caliver was just an all round handier piece of kit. Also the Irish liked to fire at close range where its armour piercing abilities were at their best.