In this paper two complex wavelet transforms, namely the Gabor wavelet transform and Kingsbury's Dual-Tree Complex wavelet transform (DT-CWT) are compared for their capabilities to extract facial features. The Gabor wavelets extract directional features from images and find frequent applications in computer vision problems of face detection and face recognition. The transform involves convolving an image with an ensemble of Gabor kernels, scale and directionally parameterized. As a result, a redundant image representation is obtained, where the number of transformed images is equal to the number of Gabor kernels used. However, repetitive convolution with 2-D Gabor kernels is a rather slow computational operation. The DT-CWT is a recently suggested transform, which provides good directional selectivity in six different fixed orientations at dyadic scales with the ability to distinguish positive and negative frequencies. It has a limited redundancy of four for images and is much faster than the Gabor transform to compute. Therefore, it arises as a good candidate to replace Gabor transform in applications, where the speed (i.e. on-line implementation) is a critical issue. We involve the two wavelet families in facial landmarks detection and compare their performance by statistical tests, e.g. by building Receiver Operating Characteristic (ROC) curves and by measuring the sensitivity of a particular feature extractor. We also compare results of Bayesian classification for the two families of feature extractors involved.