Feature engineering remains essential for tabular data analysis, and Large Language Models (LLMs) have emerged as a promising paradigm for automating this process, giving rise to LLM-powered AuTomated Tabular feature Engineering (LATTE). However, the absence of standardized platforms prevents fair, cost-aware comparisons. Furthermore, complex methodological designs obscure the specific contributions of individual components; for example, although LFG integrates Tree-of-Thought, few-shot demonstrations, Monte Carlo Tree Search, and natural language generation, the isolated impact of each technique's competitive edge remains unquantified. To address these challenges, we introduce LATTEArena, the first competitive evaluation framework featuring: (1) a six-dimensional taxonomy decomposing 15 representative methods into reusable components; (2) a standardized modular arena for controlled comparison; (3) multi-dimensional assessments covering performance, cost, and robustness; and (4) component-level ablation quantifying each technique's competitive edge. Through extensive evaluations, we reveal 16 key findings, including: (1) Tree-of-Thought with Monte Carlo Tree Search achieves optimal cost-effectiveness; (2) RPN and Code output formats dominate classification and regression tasks, respectively. We publicly release the modular framework and over 4000 execution logs, enabling researchers to seamlessly pit new techniques against existing ones and advance LATTE.