We studied how personality differences and conversation topics predict interpersonal speech coordination, leading/following dynamics, and nonverbal interactional dominance in dyadic conversations. In a laboratory, 100 undergraduate students (50 same-gender dyads) had a 15-min conversation following three topics (introduction/self-disclosure/argumentation). Their speech coordination and turn-taking (speech/silence) dynamics were assessed through nonlinear time-series analyses: Cross-Recurrence Quantification Analysis (CRQA), Diagonal Cross-Recurrence Profiles (DCRP), and Anisotropic-CRQA. From the time series, we extracted five variables to operationalize speech coordination (global and at lag-zero), leading-following dynamics, and asymmetries in the interacting partners' nonverbal interactional dominance. Interaction appraisals were also assessed. Associations between personality traits Extraversion/Agreeableness, speech coordination, and nonverbal interactional dominance were tested using mixed-effects models. Speech coordination and nonverbal interactional dominance differed across conversational topics and peaked during argumentative conversations. Extraversion was associated with increased speech coordination, and nonverbal interactional dominance, especially during the argumentative conversation. During a self-disclosure conversation, Extraversion concordance was associated with more symmetry in turn-taking dynamics. Speech coordination was generally associated with positive post-conversational appraisals such as wanting to meet in the future or liking the conversation partner, especially in extroverted individuals, whereas introverts seemed to value less swift dynamics. High Agreeableness predicted less speech coordination during argumentative conversations, and increased speech coordination (at lag-zero) predicted reduced perceived naturality in agreeable individuals. This may suggest a trade-off between maintaining swift speech dynamics and the natural flow of conversation for individuals high in Agreeableness.