[agere_contra]

I strongly suspect Henry VII.

Of course, if Henry VII had killed them, it would have been very unwise indeed for Shakespeare to write a play about Henry VII's murder of the princes, even if he had known it to be true.

Elizabeth I would have had Shakespeare rendered to Richard Topcliffe to have his gonads removed.

IIRC Shakespeare based his play on the official Tudor version of history. This incorporated Bishop Morton's vicious polemic against the dead Richard III. We can't treat Shakespeare's play as impartial evidence.

[agere_contra]

From a character point of view: the actions of the two kings while in office speak volumes.

Richard III introduced the concept of bail; allowing men freedom from jail until proven guilty.

Henry VII on the other hand invented the star chamber (a system of secret trial!).