Background Many public health departments use record linkage between surveillance data and external data sources to inform public health interventions. However, little guidance is available to inform these activities, and many health departments rely on deterministic algorithms that may miss many true matches. In the context of public health action, these missed matches lead to missed opportunities to deliver interventions and may exacerbate existing health inequities. Objective This study aimed to compare the performance of record linkage algorithms commonly used in public health practice. Methods We compared five deterministic (exact, Stenger, Ocampo 1, Ocampo 2, and Bosh) and two probabilistic record linkage algorithms (fastLink and beta record linkage [BRL]) using simulations and a real-world scenario. We simulated pairs of datasets with varying numbers of errors per record and the number of matching records between the two datasets (ie, overlap). We matched the datasets using each algorithm and calculated their recall (ie, sensitivity, the proportion of true matches identified by the algorithm) and precision (ie, positive predictive value, the proportion of matches identified by the algorithm that were true matches). We estimated the average computation time by performing a match with each algorithm 20 times while varying the size of the datasets being matched. In a real-world scenario, HIV and sexually transmitted disease surveillance data from King County, Washington, were matched to identify people living with HIV who had a syphilis diagnosis in 2017. We calculated the recall and precision of each algorithm compared with a composite standard based on the agreement in matching decisions across all the algorithms and manual review. Results In simulations, BRL and fastLink maintained a high recall at nearly all data quality levels, while being comparable with deterministic algorithms in terms of precision. Deterministic algorithms typically failed to identify matches in scenarios with low data quality. All the deterministic algorithms had a shorter average computation time than the probabilistic algorithms. BRL had the slowest overall computation time (14 min when both datasets contained 2000 records). In the real-world scenario, BRL had the lowest trade-off between recall (309/309, 100.0%) and precision (309/312, 99.0%). Conclusions Probabilistic record linkage algorithms maximize the number of true matches identified, reducing gaps in the coverage of interventions and maximizing the reach of public health action.