The integration of artificial intelligence (AI) continues to increase and evolve, including in software engineering (SE). This integration sometimes involves processes traditionally entrusted to humans, such as coding. However, the impact on socio-technical processes like code review remains underexplored. In this interview-based study (20 interviewees), we investigate how software engineers perceive and engage with Large Language Model (LLM)-assisted code reviews compared to peer-led reviews. In this inherently human-centric process, we aim to understand how software engineers navigate the introduction of AI into collaborative workflows. We found that engagement in code review is multi-dimensional, spanning cognitive, emotional, and behavioral dimensions. The introduction of LLM-assisted review impacts some of these attributes. For example, there is less need for emotional regulation and coping mechanisms when dealing with an LLM compared to peers. However, the cognitive load sometimes is higher in dealing with LLM-generated feedback due to its excessive details. Software engineers use a similar sense-making process to evaluate and adopt feedback suggestions from their peers and the LLM. However, the LLM feedback adoption is constrained by trust and lack of context in the review. Our findings contribute to a deeper understanding of how AI tools are impacting SE socio-technical processes and provide insights into the future of AI-human collaboration in SE practices.