The success of generative models for online signature verification has motivated many research works on this topic. These systems may use hidden Markov models (HMMs) in two different modes: user-specific HMM (US-HMM) and user-adapted universal background models (UBMs) (UA-UBMs). Verification scores can be obtained from likelihood ratios and a distance measure on the Viterbi decoded state sequences. This paper analyzes several factors that can modify the behavior of these systems and which have not been deeply studied yet. First, we study the influence of the feature set choice, paying special attention to the role of dynamic information order, suitability of feature sets on each kind of generative model-based system, and the importance of inclination angles and pressure. Moreover, this analysis is also extended to the influence of the HMM complexity in the performance of the different approaches. For this study, a set of experiments is performed on the publicly available MCYT-100 database using only skilled forgeries. These experiments provide interesting outcomes. First, the Viterbi path evidences a notable stability for most of the feature sets and systems. Second, in the case of US-HMM systems, likelihood evidence obtains better results when lowest order dynamics are included in the feature set, while likelihood ratio obtains better results in UA-UBM systems when lowest dynamics are not included in the feature set. Finally, US-HMM and UA-UBM systems can be used together for improved verification performance by fusing at the score level the Viterbi path information from the US-HMM system and the likelihood ratio evidence from the UA-UBM system. Additional comparisons to other state-of-the-art systems, from the ESRA 2011 signature evaluation contest, are also reported, reinforcing the high performance of the systems and the generality of the experimental results described in this paper.