Conversational automatic speech recognition remains challenging due to overlapping speech, far-field noise, and varying speaker counts. While recent LLM-based systems perform well on single-speaker benchmarks, their robustness in multi-speaker settings is unclear. We systematically compare LLM-based and modular pipeline approaches along four axes: overlap robustness, semantic fidelity, speaker count, and single- versus multi-channel input. To capture meaning-altering errors that conventional metrics miss, we introduce tcpSemER, which extends tcpWER by replacing Levenshtein distance with embedding-based semantic similarity. We further decompose tcpWER into overlapping and non-overlapping components for finer-grained analysis. Experiments across three datasets show that LLM-based systems are competitive in two-speaker settings but degrade as speaker count and overlap increase, whereas modular pipelines remain more robust.