Biometric signature verification has been traditionally performed in pen-based office-like scenarios using devices specifically designed for acquiring handwriting. However, the high deployment of devices such as smartphones and tablets has given rise to new and thriving scenarios for signature biometrics where handwriting can be performed using not only a pen stylus but also the finger via touch interaction. Some preliminary studies have highlighted the challenge of this new scenario and the necessity of further research on the topic. The main contribution of this work is to propose a new on-line signature verification architecture adapted to the signature complexity in order to tackle this new and challenging scenario. Additionally, an exhaustive comparative analysis of both pen- and touch-based scenarios using our proposed methodology is carried out along with a review of the most relevant and recent studies in the field. Significant improvements of biometric verification performance and practical insights are extracted for the application of signature verification in real scenarios.