The two of them would be good casting for the lead two roles in Becket. I’ve read that Burton and O’Toole also played these roles on stage and on occasion switched roles(O’Toole played Becket and Burton played Henry II).
Actually, neither played it onstage. In fact, it's a sore subject with the Royal Shakespeare Company, who bought the rights to the play in order that O'Toole could play the king. However, O'Toole opted instead to break his RSC contract and do Lawrence of Arabia instead. It was particularly galling to the RSC that O'Toole ended up doing the film after stiffing them on the play (they got Christopher Plummer to replace O'Toole onstage).
The original broadway stars were Olivier and Anthony Quinn. Olivier figured out during the run that Henry II was the flashier part; so when Quinn left the play (also to appear in Lawrence), Olivier took the part of the king and Arthur Kennedy played Becket. Ironically, Kennedy's next role was to replace the ailing Edmund O'Brien in....Lawrence of Arabia.