Dam-break flows pose significant challenges for accurate and efficient hydrodynamic prediction. This study comprehensively evaluated three DeepONet architectures (vanilla DeepONet, physics-informed DeepONet (PI-DeepONet), and Markov DeepONet (M-DeepONet)) for simulating dam-break hydrodynamics. Extensive numerical experiments exhibited that vanilla DeepONet achieved the highest accuracy, with errors corresponding to only 37.9% and 17.5% of the errors produced by M-DeepONet and PI-DeepONet, respectively. Meanwhile, vanilla DeepONet maintained superior computational efficiency, with a computational duration equivalent to 17.19% of that required by the conventional numerical algorithm. However, its performance was highly dependent on the quantity of training data, with errors increasing by 95.08% as the sampling rate decreased from 100% to 10%. PI-DeepONet exhibited exceptional robustness under data-scarce conditions, with errors amounting to only 24.75% of those observed in vanilla DeepONet at 10% sampling, and it remained stable under high-noise conditions, showing just a 21.9% error increase. M-DeepONet balanced accuracy with sequential prediction capability but suffered from error accumulation in noisy scenarios. These findings reveal distinct trade-offs: vanilla DeepONet excels in data-rich high-accuracy applications, whereas PI-DeepONet is optimal when data are limited or corrupted by noise. This study provides actionable guidelines for model selection in disaster prediction systems, advances operator learning in hydrodynamics, and bridges critical gaps between theoretical development and practical engineering applications.