In this study, we analyze automatic evaluation metrics for Natural Language Generation (NLG), specifically task-agnostic metrics and human-aligned metrics. Task-agnostic metrics, such as Perplexity, BLEU, BERTScore, are cost-effective and highly adaptable to diverse NLG tasks, yet they have a weak correlation with human. Human-aligned metrics (CTC, CtrlEval, UniEval) improves correlation level by incorporating desirable human-like qualities as training objective. However, their effectiveness at discerning system-level performance and quality of system outputs remain unclear. We present metric preference checklist as a framework to assess the effectiveness of automatic metrics in three NLG tasks: Text Summarization, Dialogue Response Generation, and Controlled Generation. Our proposed framework provides access: (i) for verifying whether automatic metrics are faithful to human preference, regardless of their correlation level to human; and (ii) for inspecting the strengths and limitations of NLG systems via pairwise evaluation. We show that automatic metrics provide a better guidance than human on discriminating system-level performance in Text Summarization and Controlled Generation tasks. We also show that multi-aspect human-aligned metric (UniEval) is not necessarily dominant over single-aspect human-aligned metrics (CTC, CtrlEval) and task-agnostic metrics (BLEU, BERTScore), particularly in Controlled Generation tasks.