Depression is the most common psychological disorder and is considered as a leading cause of disability and suicide worldwide. An automated system capable of detecting signs of depression in human speech can contribute to ensuring timely and effective mental health care for individuals suffering from the disorder. Developing such automated system requires accurate machine learning models, capable of capturing signs of depression. However, state-of-the-art models based on deep acoustic representations require abundant data, meticulous selection of features, and rigorous training; the procedure involves enormous computational resources. In this work, we explore the effectiveness of two different acoustic feature groups - conventional hand-curated and deep representation features, for predicting the severity of depression from speech. We explore the relevance of possible contributing factors to the models' performance, including gender of the individual, severity of the disorder, content and length of speech. Our findings suggest that models trained on conventional acoustic features perform equally well or better than the ones trained on deep representation features at significantly lower computational cost, irrespective of other factors, e.g. content and length of speech, gender of the speaker and severity of the disorder. This makes such models a better fit for deployment where availability of computational resources is restricted, such as real time depression monitoring applications in smart devices.