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Context. Radio pulsars can be used for many studies, including the investigation of the ionized interstellar medium and the solar wind via their dispersive effects. These phenomena affect the high-precision timing of pulsars and are among the main sources of noise in experiments searching for low-frequency gravitational waves in pulsar data. Aims. In this paper, we compare the functionality and reliability of three commonly used schemes to measure temporal variations in interstellar propagation effects in pulsar timing data. Methods. We carried out extensive simulations at low observing frequencies (100–200 MHz) by injecting long-term correlated noise processes with power-law spectra and white noise, to evaluate the robustness, accuracy, and precision of the following three mitigation methods: epoch-wise (EW) measurements of interstellar dispersion; the DMX method of simultaneous, piece-wise fits to interstellar dispersion; and DM GP, which models dispersion variations through Gaussian processes using a Bayesian analysis method. We then evaluated how reliably the input signals were reconstructed and how the various methods reacted to the presence of achromatic long-period noise. Results. All the methods perform well, provided the achromatic long-period noise is modeled for DMX and DM GP. The most precise method is DM GP, followed by DMX and EW, while the most accurate is EW, followed by DMX and DM GP. We also tested different scenarios including simulations ofL-band times of arrival and realistic DM injection, with no significant variation in the obtained results. Conclusions. Given the nature of our simulations and our scope, we deem that EW is the most reliable method to study the Galactic ionized media. Follow-up works should be conducted to confirm this result via more realistic simulations. We note that DM GP and DMX seem to be the best-performing techniques in removing long-term correlated noise, and hence for gravitational wave studies. However, full simulations of pulsar timing array experiments are needed to support this interpretation.