Following on from the mention of Edward IV on Peer Review this week.
Richard III considered that Edward's marriage to Elizabeth Woodville was invalid as Edward had entered into a marriage contract previously, with Lady Eleanor Butler, (probably as a pre-requisite to get her into his bed). Thus Edward's children, including the Princes in the Tower, were illegitimate, and so Edward V could not become king. Richard didn't have to worry about their claim to the throne.
On the other hand, Henry VII wanted to bolster his tenuous claim by marrying the Princes' sister, Elizabeth. She would have to be declared legitimate for this to have any point. However this would then make Edward V the legitimate king. Henry thus had a much better reason to dispose of the princes.
The Tudors also suppressed the evidence that Edward IV himself was illegitimate, again to legitimise Elizabeth.