Modern distributed systems generate large volumes of logs that can be analyzed to support essential AIOps tasks such as fault diagnosis, which plays a crucial role in maintaining system reliability. Most existing approaches rely on log-based models that treat logs as linear sequences of events. However, such representations discard the structural context between events that are often present in execution logs, such as parent-child dependencies, fan-out (branching), or temporal features. To better capture these relationships, recent works on Graph Neural Networks (GNNs) suggest that representing logs as graphs offers a promising alternative. Building on these observations, this paper conducts a comparative study of log-based encoder architectures (e.g., BERT) and graph-based models (e.g., GNNs) for automated fault diagnosis. We evaluate our models on TraceBench, a trace-oriented log dataset, and on BGL, a more traditional system log dataset, covering both anomaly detection and fault type classification. Our results show that graph-only models fail to outperform encoder baselines. However, integrating learned representations from log encoders into graph-based models achieves the strongest overall performance. These findings highlight conditions under which graph-augmented architectures can outperform traditional log-based approaches.