Much has been written about duty-interest conflicts but very little by way of duty-duty conflicts, although both topics will form part of my thesis.
After assessing how duty-interest conflicts are regulated, which also appears inconsistent in itself, it is appears that such regulation would not cover substantially duty-duty conflicts for directors.
Dr. Matthew Conaglen has written substantially on the topic however, my work is in reference to the fiduciary relationship between director-company which has fundamental differences from that of other fiduciary relationships.
S.175(7) of the Companies Act 2006 does try to address duty-duty conflicts:
(7) Any reference in this section to a conflict of interest includes a conflict of interest and duty and a conflict of duties
The section clearly treats duty-duty conflicts as something "additional" to duty-interest conflicts rather than its own separate principle.
Notably in the parliamentary debates in the Grand Committee a lot of the discussion focused on directors serving on more than one board when referring to s175, which is clearly a duty-duty conflict, however they were talking about it in reference to s175 and duty-interest conflicts. This perhaps demonstrates the vagueness of the principle or a reluctance to allow it to be its own principle.
Few cases have made reference to the duty-duty conflicts. Most read so far, i.e. the case of Mothew, usually refer to where the fiduciary's two principals are contracting with one another in some way. None seem to make reference to a case regarding opportunities coming to a director that could be taken by either principal. Directors are restricted by the "double management" rule (meaning they cannot serve on competing boards) but with the interconnected firms growing, e.g. Steve Jobs serving on Apple's board and Disney's board, the duty-duty conflict may become more relative in years to come.