(It should be someone like James Fenimore Cooper to compose this reaction piece but I will do my best.)
Daenerys Targaryen is a better ruler and leader than Jon Snow. We are all familiar with their leadership styles. There is enough information for us to pass judgment on who the better leader is. I will start with Jon Snow.
Jon is far from the worst leader in A Song of Ice and Fire. He is actually capable most of the time. His biggest strength as a leader is his ability to teach. Jon was able to teach the other less-fortunate cadets the proper use of the sword in combat. Yes, he was an arrogant and entitled fool when he arrived. A little man to man talk with a seasoned man helped open his eyes. Many of the fans praise Jon for protecting the craven cadet, Samwell Tarly. It is a well-earned praise. Samwell would have died from fright if Jon had not stepped in and helped.
I have established that Jon Snow is basically an average guy who has had a good training in the fighting arts. As a leader, he is usually capable of performing his job. However, there problems beneath his exterior. Many of the fans have already brought it up repeatedly. Jon has a chip on his shoulders. Push that chip and he goes ballistic. He is guilty of attacking Ser Alliser Thorne, a superior officer. He has anger management issues which culminated in the inappropriate way in which he judged two guilty men, Janos Slynt and Mance Rayder. By every laws of the land, it should have been the deserter and turncloak, Mance Rayder, who was executed. Matters went downhill from there. He sent the deserter and turncloak to bring his sister to him at the Wall. This is an act of war against Roose and Ramsay Bolton. The Night's Watch should never, and never has until now, make war against the people of The Seven Kingdoms.
I served in the military for the better part of my early adult life. I have never been tested in the same way as Jon was with Arya. I will say there are a lot of men who would do as Jon did. They would forsake their duties, no matter how critical it is, to save their sisters. But there are still more who would do their duties and accept that they cannot help their sisters. For proof, you only have to look at those men who are in the business of rescuing and saving people and property. Many men would rather be at home with their families during an emergency crisis but instead they stay at their posts and do their jobs. I knew people who went to Kuwait while they had desperate families back home. Parents battling cancer. Wives struggling to raise handicapped children alone. I could go on and on. The point is, it is not unreasonable nor is it rare for people to do their jobs even when they have critical family concerns back home. And those men who can't do this should never be in command. It's fine for desk jockey to always sacrifice his duties for his families. But that is not acceptable for a commander of an organization who has been tasked with the protection of the kingdom.
Quorin Halfhand said something in book 2. He said of Mance Rayder, he was the best and the worst of us. He had trouble obeying. Jon is very much like Mance Rayder. In many ways, he is the ideal black brother. But he is also the worst possible. Jon is a man gifted with martial skills. He is a smart young man who usually makes sound decisions. I don't think his inability to judge and prioritize will matter much with the Wildlings. To the Free Folk, whatever the strong man says is right is right. Might makes right with the Wildlings. Jon does not have to be fair, nor consistent. Laws among the Wildlings are not as well-defined.
Princess Daenerys Targaryen began the story a scared and nervous young girl. Forced to marry into an alien culture, she used her natural intelligence to thrive. Courage, intelligence, and determination allowed her to adapt to the Dothraki culture. She brought the dragons back from extinction. She had the smarts and the courage to lead her khalasar beyond the Red Waste until they reached Vaes Tolorro. This is nothing less than remarkable for a girl of her age. She defeated the Undying in the Palace of Dust with the help of her dragon, Drogon. Over and over, Daenerys has managed to use her intelligence and her cunning to outmaneuver her adversaries. She has become a very good player of the game of thrones with her own style.
Queen Daenerys has become the conqueror and the ruler of the slaver city of Meereen. She knows what we know. As humans, we have a responsibility to make laws and judge the guilty. The Meereenese masters perpetrated the most heinous war crime in the entire saga so far. This is many times more heinous than the Red Wedding in The Twins. The masters crucified the children of their slaves and used them to decorate the road to the city. This kind of crime cannot go unpunished. To do so would be to deny justice to those children. Allowing the Meereenese to bring forth the guilty is a modern concept of peers judging peers. It is certainly preferable to the arbitrary trial of combat being practiced in Westeros. She is facing an enemy who refuse to fight her troops in open combat. And yet, she refused to execute her cup bearers. This was a smart move. Those children can be socialized and educated away from their slaver parents. These children will be the foundation of a free Slaver's Bay.
The situation in Meereen is very complicated. Skahaz, Reznak, and Hizdahr are unreliable allies. Daenerys has been warned to be careful by Quaithe. Yet, she reacts with reason and caution. A Cersei would have had them all killed. But a good leader knows that you have to trust people. Everything carries a risk. One person cannot manage a city of the size of Meereen. Jorah's betrayal is revealed. Daenerys wisely did not kill the man and instead sent him into exile. Daenerys is a reflective, thoughtful person. Which is a good quality for someone who has to make decisions. She has much to learn about ruling but her potential is without limits.