What characteristics of Hotspur would make him a better leader/king than Hal?

On the surface, it could easily appear that Hotspur has more of the attributes of a good king than Henry. After all, Hal seems to spend his time hanging around inns drinking with unreliable party animals like Falstaff who only want to have a good time. That certainly seems like irresponsible behavior in a person who will have a country to rule.
Also, when it comes to sheer knightly courage and rigid integrity, Hotspur seems to have it over Hal. He despises fawning courtiers and lives by rugged warrior values. His fearlessness and uncompromising values make him appear a good leader.
Hal, however, is getting better training in leadership because he is learning about the common people through interacting with them. He is developing his people skills and coming to understand what people are like when they are not putting up front for him because he is a prince. He learns to accurately judge character, and he becomes adaptable. Unlike Hotspur, he doesn't live in an unrealistic bubble. He is not so hot-headed and impulsive as his rival. In the end, he emerges as the more capable leader.

Hotspur—or, Henry Percy, to give him his real name—is the son and heir of the Earl of Northumberland. Around the same age as Prince Hal, he also has a kingly bearing about him, as one would expect from a scion of one of England's greatest noble houses. Whether that would necessarily make him a better ruler than Hal is a matter for debate. Certainly, Harry Hotspur possesses a number of qualities that would make for an excellent king. He is incredibly brave in battle, is charismatic, and has a forceful personality that easily binds others to his iron will.
Yet at the same time, Hotspur has many flaws. For one thing, his physical courage easily spills over into outright recklessness. He is rather impetuous, his fevered mind going in several different directions at once, making it almost impossible for him to stay focused on anything for very long. A lack of maturity and sound judgement is also a problem. There can be no doubt that, on the battlefield, Hotspur is second to none when it comes to sheer courage. After all, that's how he earned his nickname. But because of the serious character flaws we've just been considering, he is singularly unfitted for any position of great authority, be it general or king.
Prince Hal may be an upper-class delinquent with a yen for petty criminality and hanging out in taverns with low-lives and thieves, but crucially, he has the capacity to change. There's not much evidence to suggest that Hotspur has similar capabilities. And so, on balance, one would have to conclude that Hotspur would not have made a better king than Prince Hal.