In the absence of hard data on Germanwings’ selection and monitoring procedures, at least at the moment, (they now say they use psychological assessments) I have looked at large data sets on US fighter pilots. If one compares intelligence measures with personality inventories, then intelligence has the lead:
The predictive validity of cognitive ability and personality traits was examined in large samples of U.S. Air Force pilot trainees. Criterion data were collected between 1995 and 2008 from 4 training bases across 3 training tracks. Analyses also examined consistency in pilot aptitude and training outcomes. Results were consistent with previous research indicating cognitive ability is the best predictor of pilot training performance. There were few differences across training tracks, bases, and years, and none was large. Overall, results illustrated the consistency of the quality of pilot trainees as assessed by cognitive ability and personality trait measures, and the consistency of these measures in predicting training performance over time. This consistency results in a more stable training system, enabling greater efficiency and effectiveness.
It is probably best to look at primary training for the most representative results (after that one is progressively dealing with very good pilots) but the personality measures contribute less strongly, only in terms of Openness to Experience and Conscientiousness. If you accept the fully corrected scores in the last column of each training level then intelligence is the most substantial factor. Remember that the applicants are already highly selected for intelligence, so these correlations are surprisingly large.
Of course, being a fighter pilot is more demanding than commercial flying, but the tasks are broadly the same.