Large language models (LLMs) have demonstrated remarkable reasoning and planning capabilities, driving extensive research into task decomposition.Existing task decomposition methods focus primarily on memory, tool usage, and feedback mechanisms, achieving notable success in specific domains, but they often overlook the trade-off between performance and cost.In this study, we first conduct a comprehensive investigation on task decomposition, identifying six categorization schemes.Then, we perform an empirical analysis of three factors that influence the performance and cost of task decomposition: categories of approaches, characteristics of tasks, and configuration of decomposition and execution models, uncovering three critical insights and summarizing a set of practical principles.Building on this analysis, we propose the Select-Then-Decompose strategy, which establishes a closed-loop problemsolving process composed of three stages: selection, execution, and verification.This strategy dynamically selects the most suitable decomposition approach based on task characteristics and enhances the reliability of the results through a verification module.Comprehensive evaluations across multiple benchmarks show that the Select-Then-Decompose consistently lies on the Pareto frontier, demonstrating an optimal balance between performance and cost.Our code is publicly available at https://github.com/summervvind/ Select-Then-Decompose.