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Objectives: Manual seismic phase picking and earthquake catalog building become challenging because the number of seismic stations increases. With the rapid development of artificial intelligence, several deep learning models are developed for seismic phase picking, but their performance and applicability remain ambiguous. Methods: Phase-Net and EqT can extract relevant features at different levels from raw seismic waveforms and map them into probabilistic sequences. In this paper, the performance of these two widely-used deep learning models for earthquake detection and phase picking is investigated with the 2019 Ridgecrest earthquake (California, USA) sequence and the 2019 Weiyuan Ms 5.4 earthquake (Sichuan, China) sequence. Besides, the completeness and accuracy of the constructed earthquake catalogs are analyzed and evaluated by cross-validation. Results: The results show that the two models, though trained with datasets from different regions, perform well in cross-region applications and are comparable to manual analysis. EqT1 provides high detection precision with few false alarms, even under a low threshold. But EqT1 has a limited recall rate, implying that fewer earthquakes are detected compared with Phase-Net. The picking performance of Phase-Net is sensitive to the employed threshold. With the low and moderate thresholds, Phase-Net can detect more earthquakes than EqT1 and manual catalog, while registering a relatively low detection precision. With the high threshold, the precision of Phase-Net is comparable to that of EqT1. EqT2 is not recommended due to its inferior performance over EqT1 and Phase-Net. Conclusions: EqT1 provides a higher precision when being employed for seismic phase picking, leading to earthquake catalogs with better accuracy. Phase-Net has a higher recall rate and generates more complete catalogs. Both models can facilitate automatic and rapid construction of earthquake catalogs. [ABSTRACT FROM AUTHOR]