I have been training for du's for the last 4 yrs .. no amazing results but usually in the top 1/3 of my age group (35-40) and have been asking myself this question for quite a while, ocnsidering that we have limited amount of time dedicated to training (+ family and work), should we split our training equaliy to both sports (running and cycling) or slight favor one (the strong one or the weak one) ?? I guess you could also ask the same question within the sport (ie cycling hills or flats)
The old saying is "train your weakness, race your strength". But that doesn't mean neglecting your strong points, not by a long shot. Perhaps doing focused exercises to bring up your weakness (like Greg Lemond doing weekly sprint training even though he is not a natural sprinter) as part of a balanced training program.
For the duathlon training, I don't know much about it except that the guy I was riding with last night says that weekly running seems to keep his muscles in shape for competing in du's while near-daily riding keeps his fitness up for both activities and is better for buggy sweltering summer weather than running. YMMV.