Code review is a socio-technical practice, yet how software engineers engage in Large Language Model (LLM)-assisted code reviews compared to human peer-led reviews is less understood. We report a two-phase qualitative study with 20 software engineers to understand this. In Phase I, participants exchanged peer reviews and were interviewed about their affective responses and engagement decisions. In Phase II, we introduced a new prompt matching engineers' preferences and probed how characteristics shaped their reactions. We develop an integrative account linking emotional self-regulation to behavioral engagement and resolution. We identify self-regulation strategies that engineers use to regulate their emotions in response to negative feedback: reframing, dialogic regulation, avoidance, and defensiveness. Engagement proceeds through social calibration; engineers align their responses and behaviors to the relational climate and team norms. Trajectories to resolution, in the case of peer-led review, vary by locus (solo/dyad/team) and an internal sense-making process. With the LLM-assisted review, emotional costs and the need for self-regulation seem lower. When LLM feedback aligned with engineers' cognitive expectations, participants reported reduced processing effort and a potentially higher tendency to adopt. We show that LLM-assisted review redirects engagement from emotion management to cognitive load management. We contribute an integrative model of engagement that links emotional self-regulation to behavioral engagement and resolution, showing how affective and cognitive processes influence feedback adoption in peer-led and LLM-assisted code reviews. We conclude that AI is best positioned as a supportive partner to reduce cognitive and emotional load while preserving human accountability and the social meaning of peer review and similar socio-technical activities.