Event camera offers substantial advantages over conventional video cameras with their efficiency, extremely high temporal resolutions, low latency, and high dynamic range. These benefits have led to applications in various vision domains. Recently they have been applied in facial recognition tasks as well. However, while significant advantages of event cameras in some facial processing tasks have been demonstrated, the initial stage in almost any task, i.e., face alignment, is not at par with the conventional cameras. This study investigates the use of face alignment convolutional networks regarding both performance and complexity for event camera processing. Our aim is event camera face pose alignment that can be used as an efficient preprocessor for facial tasks. Therefore, we comparatively evaluate simple convolutional coordinate regression with a hybrid of coordinate and heatmap regression, known as pixel-in-pixel regression. Our experimental results reveal the superior performance of the hybrid method. However, we also show that if there is a computation bottleneck, simple convolutional coordinate regression is preferable for their low resource requirements though at the expense of some performance loss.