Motivation: Public health authorities can provide more effective and timely interventions to protect populations during health events if they have effective multi-purpose surveillance systems. These systems rely on aberration detection algorithms to identify potential threats within large datasets. Ensuring the algorithms are sensitive, specific and timely is crucial for protecting public health. Here, we evaluate the performance of three detection algorithms extensively used for syndromic surveillance: the 'rising activity, multilevel mixed effects, indicator emphasis' (RAMMIE) method and the improved quasi-Poisson regression-based method known as 'Farrington Flexible' both currently used at Public Health England, and the 'Early Aberration Reporting System' (EARS) method used at the US Centre for Disease Control and Prevention. We model the wide range of data structures encountered within the daily syndromic surveillance systems used by PHE. We undertake extensive simulations to identify which algorithms work best across different types of syndromes and different outbreak sizes. We evaluate RAMMIE for the first time since its introduction. Performance metrics were computed and compared in the presence of a range of simulated outbreak types that were added to baseline data. Results: We conclude that amongst the algorithm variants that have a high specificity (i.e. >90%), Farrington Flexible has the highest sensitivity and specificity, whereas RAMMIE has the highest probability of outbreak detection and is the most timely, typically detecting outbreaks 2-3 days earlier.