I asked Colin Baker about this, actually. He said that it should just be treated as a coincidence, and that there was not meant to be any deeper connection between the characters. (This was right after Baker was fired from the show, but he was very enthusiastic toward the show's fans, and he was very candid about everything that had happened surrounding his difficult tenure on Doctor Who.)
The out-of-universe reason was that John Nathan-Turner was impressed by Baker when he played Maxil in "Arc of Infinity," and that was where Nathan-Turner got the idea of casting Baker as the next Doctor. Producing Doctor Who was Nathan-Turner's first job as part of the creative staff of a television show; he had extensive credits previously, but only in logistics and financial management of shows. One downside of this was that Nathan-Turner did not have close relationships with very many actors. This was reflected in his casting both of Peter Davison (Nathan-Turner had been production unit manager on Davison's previous show All Creatures, Great and Small) and Colin Baker, who had so impressed the producer during "Arc of Infinity"; they were among the relatively small stable of actors he had worked with closely.
Ironically, the traits that got Colin Baker the role of The Doctor may have ended up being irrelevant to how he played the role. Both of the characters Baker played on Doctor Who were quite hard edged, while in person, Colin Baker had an extremely funny and charming personality.