Population-adjusted indirect comparisons are used to estimate treatment effects when there are cross-trial differences in effect modifiers and when access to individual patient data is limited. Increasingly, health technology assessment agencies are accepting evaluations that use these methods across a diverse range of therapeutic areas. Popular methods include matching-adjusted indirect comparison (MAIC) and simulated treatment comparison (STC). Despite this increasing popularity, there is limited formal evaluation of these methods and whether they can be used to accurately compare treatments. Thus, we undertake a comprehensive simulation study to compare standard unadjusted indirect comparisons, MAIC and STC across 162 scenarios. This simulation study assumes that the trials are investigating survival outcomes and measure binary covariates, with the log hazard ratio as the measure of effect. This is one of the most widely used setups in health technology assessment applications. The simulation scenarios vary the trial sample size, prognostic variable effects, interaction effects, covariate correlations and covariate overlap. Generally, MAIC yields unbiased treatment effect estimates, while STC is often biased with non-linear link functions and may overestimate variability. Standard indirect comparisons are systematically biased, particularly under stronger covariate imbalance and interaction effects. Coverage rates are valid for MAIC. Interval estimates for the standard indirect comparison are too narrow and STC suffers from overcoverage or from bias-induced undercoverage. MAIC provides the most accurate estimates and, with lower degrees of covariate overlap, its bias reduction outweighs the loss in effective sample size and precision.