One of the big reasons Henry VII won at Bosworth was that Richard was betrayed. Several nobles with their armies showed up and promised to fight with him only to watch from a bit off while richard and his men were slaughtered by A force much stronger than his. If they had fought, as promised, very likely Richard would have won. Even Richards meanest enemies admitted he was a good military man. His main failing as a King was that he wasn't ruthless enough. If youre King of england you have to be ruthless to stay king of england. Both Henry VII and Henry VIII was ruthless enough. Rgey did not leave threats against the throne alive for long. Richard know who his adversaries were both didn't do anything against them. There were short rebellioins in both1483 and 1484 and if he had rgrown them in jail then, as most other kings did in europe, Henry wouldn't have been able to gain as much support as he did in 1485. Richard was naive, not really King material.. He had been exceedingly loyal towards his brother when he was King and Edward trusted him completely. But when he took a step up and tried to rule with all the court jealosies and hatreds that existed he wasn't tough enough to handle that.
When it comes to Richard I, the Lionheart, he was a great commander of armies but as a King of England i wouldn't rank him so high. He spent under a year total in England during the years of his reign. Other wise in the holy land, captured in Germany or in France. He never really cared a lot about england but cared a lot about his duchy in aquitaine that he inherited from his mother. For him it was always Aquitaine first, England second. So, as just Kings of England, i would rank both Edward I and Edward III higher. They were ruthless towards the scots, yes but if we see them just as english monarchs they were extremely successful.