I would suggest that the polarizing nature of their reputations is due in large part to their political successes/failures. Richard became famous for his crusades and battles against the Sultan Saladin (despite having only really 1 successful battle at Acre). When Richard was not waging war in the holy land he was constantly beating his French opponent Philip Augustus. Richard had inherited the expansive Angevin empire from his father Henry II, and Richard saw the zenith of its growth due to his crusading success (which allowed him to tax like crazy for war efforts against the French), and his military successes against Philip II. Richard was much like his father Henry II in that he was a very militaristic King and was constantly outmaneuvering his opponents.

Now, contrast that with John. John presided over the complete and utter collapse of the Angevin empire, losing virtually all of the Angevin lands in France with the exception of Bordeux in southwest france (a small part of the duchy of Aquitaine acquired by Henry II marriage to Eleanor of Aquitaine). John was nothing like his brother or his father in terms of military experience and temperament. He was viewed politically as a snake, and was very paranoid about everyone's perception of him. Due to his massive military failures and losses in France the nobility and the gentry wouldn't support any more taxation for his failed military endeavors. John continued to squeeze out as much as he could in other ill-conceived ways (in two examples he would charge enormous fees for children to inherit their father's titles, as well as charge enormous fees for widow's to be able to remarry). Ultimately this led to many of John's Baron's rising up in revolt and eventually forcing him to sign the Magna Carta at Runnymede.

In terms of answering the question of hero vs. villian I suppose it boils down to how you define those terms. Richard was an absolutely outstanding medieval king, which is to say he was brutal to his enemies (his crusades were notoriously bloodthirsty affairs), was very charismatic with his people (and they loved him for his military successes despite his incredible taxation burden that he placed on his people), and was viewed as a pious king due to his crusades, and in many cases his very Anti-Semitic views. Whether that makes Richard a hero or not is really open for debate.

John was indeed a nasty character and a failed medieval monarch because of his military failures and empire losses. He is believed to have killed his nephew Arthur of Brittany in a drunken rage with his bare hands because he was paranoid that Arthur would rise up and seize the throne from him. He went out of his way to tax and seize as much money as he could throughout the kingdom, often employing very nefarious means to do so, making him at one point the wealthiest Angevin king in the history of the empire. However, arguably John in retrospect is often viewed as the villain due to his breaking of the treaty of the Magna Carta. The Magna Carta has gone down in history as one of the founding documents of democratic forms of government. However, when one really scrutinizes the document you quickly realize that the Magna Carta was simply a failed peace treaty between a tyrannical king and his baron's that did not like having their cozy political positions and wealth/power controlled and manipulated by said king. Whether or not that makes him a villain or not is still up for debate, but likely considerably less so than Richard case as the hero as John has some very nasty blemishes on his character in terms of specific acts that he did.

If you want to learn about this I strongly recommend reading a couple of different books: "Magna Carta: The Birth of Liberty" by Dan Jones. "The Plantagenets: The Warrior Kings and Queens Who Made England" by Dan Jones.

And one of my personal favorites: "The Greatest Knight" by Thomas Asbridge This one tells the story of William Marshall who's medieval career is nothing but absolutely astonishing, and makes most other characters pale in comparison to his accomplishments. William is arguably the model image of knighthood within the context of medieval chivalry. This book would be good for a direct answer to your question as William served under both King Richard and King John.