This is one of those rather pointless arguments, since the answer to the question really depends upon the individual in question. Both cardio- vascular fitness and adequate amounts of muscular strength/endurance are necessary for optimum human function, but that doesn't mean that any individual need develop elite levels of fitness in each area.
Aerobic fitness has always weighed heavily on peoples' minds for two main reasons - reduction in cardiovascular disease risk and the age-related decline in VO2max and the subsequent reduction in functional capacity.
More and more data is amassing that demonstrates that cardiovascular disease risk can be substantially reduced merely by engaging in daily, low-level activity - the sort that won't make you aerobically fit, but will involve getting off the couch and moving around a bit. Certainly someone who weight trains on a regular basis and maintains even a moderate activity level on other days would fit this profile, with or without aerobic training.
As for the age-related decline in VO2max, while aerobic fitness may certainly be a factor, recent evidence suggests that "sarcopenia" (lack of lean muscle tissue) may be the real culprit, and that the declining VO2max is secondary to the changes in body composition that occur in the sedentary aging population. Both low aerobic fitness levels and muscle weakness can impair the function of the elderly, and often the short-term gains from a strength training program (which will include not only increased muscle strength/endurance but a concomitant increase in functional capacity) will provide better pay-off than the more traditional cardiovascular exercise prescription for this population (especially since the CVD risk-reduction is more of a long-term effect than a short one).
While almost any exercise prescription will include both aerobic and anaerobic components, the exact balance can vary considerably. In some instances, such as the desire to avoid overtraining in a previously sedentary senior population, strength training may take priority, and any additional aerobic training prescribed may "fill in the cracks" rather than take center stage.
With an elite endurance athlete, of course, the situation might be reversed. Runners, for example, can benefit from strength workouts, but the shape of the strength training workout will be dictated by the needs of their aerobic training and not the other way around.
In the end, our goal is to improve human function. Who the human is will help us decide what function we're trying to improve.