The play Richard II is one of Shakespeare's History Plays and, therefore, isn't bound to the requirements of tragedy. This is an interesting fact to note, because it releases the reader from needing to cast either Richard or Henry as Hero or Villain of the story. Richard was, in real life, king; and Henry, in real life, did contest his rule and win the crown for himself.
The play, rather than concerning itself so much with an examination of the internal workings of either character as the "central" figure, aims to explore the nature of rulership itself. What does a king need to be considered a wise and just ruler? Should a king's right to rule be considered "divine"--that it, is it God that, by birth, confers kingship, or should it be assigned according to the qualities of the man?
In this play, Richard is seen as the debauched ruler. Favoring some of his advisors over others, taxing his people to pay for his own pleasures, concerning himself more with the pomp and circumstance of his position, rather than the hard work of governance. He does not have the favor of the people.
In contrast, Henry is quite the common folks' favorite. He acts swiftly and with purpose in order to render judgement in a morally upright and honest way. He is highly involved and invested in the workings of the government, rather than simply enjoying title and privilege.
For more on these two fasicinating characters, please follow the links below.