The only point of reference I can think of is the end of hammered coinage and its replacement with an all milled coinage. Good question, never noticed or thought about it. However, thinking about it now.........
One possible reason could be that Charles I faced left, so you would expect Charles II to face right (the Commonwealth didn't exist in Royalist eyes, Charles II's accession being on the death of his father). The Cromwell and hammered Charles II coins faced left, but as any royal succession out of the question with the abolition of the monarchy, the custom of alternating busts became irrelevant. Moreover, the latter two issues were engraved by Thomas Simon. As one who worked for Cromwell et al, he may not have cared which way Charles II faced. The odd ones out are the Commonwealth, Cromwell and Chas.2 hammered issues.