Large Language Models (LLMs) are increasingly deployed in both academic and industry settings to automate the evaluation of information seeking systems, particularly by generating graded relevance judgments. Previous work on LLM-based relevance assessment has primarily focused on replicating graded human relevance judgments through various prompting strategies. However, there has been limited exploration of alternative assessment methods or comprehensive comparative studies. In this paper, we systematically compare multiple LLM-based relevance assessment methods, including binary relevance judgments, graded relevance assessments, pairwise preference-based methods, and two nugget-based evaluation methods~--~document-agnostic and document-dependent. In addition to a traditional comparison based on system rankings using Kendall correlations, we also examine how well LLM judgments align with human preferences, as inferred from relevance grades. We conduct extensive experiments on datasets from three TREC Deep Learning tracks 2019, 2020 and 2021 as well as the ANTIQUE dataset, which focuses on non-factoid open-domain question answering. As part of our data release, we include relevance judgments generated by both an open-source (Llama3.2b) and a commercial (gpt-4o) model. Our goal is to \textit{reproduce} various LLM-based relevance judgment methods to provide a comprehensive comparison. All code, data, and resources are publicly available in our GitHub Repository at https://github.com/Narabzad/llm-relevance-judgement-comparison.