Context. To date, stellar activity is one of the main limitations in detecting small exoplanets via transit photometry. Since this activity is enhanced in young stars, traditional filtering algorithms may severely under-perform in detecting such exoplanets. Aims.This paper aims to compare the relative performances of four algorithms developed by independent research groups specifically for the filtering of activity in the light curves (LCs) of young active stars, prior to the search for planetary transit signals: Notch and LOCoR(N&L), Young Stars Detrending(YSD), K2 Systematics Correction(K2SC) and VARLET. We include in the comparison also the two best-performing algorithms implemented in Wotan, namely the Tukey's biweight and the Huber Spline. Methods. We performed a series of injection-retrieval tests of planetary transits of different types, from Jupiter down to Earth-sized planets, moving both on circular and eccentric orbits. The tests were carried out over 100 simulated LCs of both quiet and active solar-like stars that will be observed by the ESA space telescope PLATO. Results. We found that N&L is the best choice in many cases, since it misses the lowest number of transits. However, it under-performs if the planetary orbital period closely matches the stellar rotation period, especially in the case of small planets for which the biweight and VARLET algorithms work better. For LCs with a large number of data, the combined results of YSD and Huber Spline yield the highest recovery percentage. Filtering algorithms allow us to get a very precise estimate of the orbital period and the mid-transit time of the detected planets, while the planet-to-star radius is under-estimated most of the time, especially in the case of grazing transits or eccentric orbits. A refined filtering taking into account the presence of the planet is compulsory for a proper planetary characterization.