We discuss the role that dwarf galaxies may have played in the formation of the Galactic halo (Halo) using RR Lyrae stars (RRL) as tracers of their ancient stellar component. The comparison is performed using two observables (periods, luminosity amplitudes) that are reddening and distance independent. Fundamental mode RRL in 6 dwarf spheroidals (dSphs) and 11 ultra faint dwarf galaxies (~1300) show a Gaussian period distribution well peaked around a mean period of langPabrang = 0.610 ± 0.001 days (σ = 0.03). The Halo RRL (~15,000) are characterized by a broader period distribution. The fundamental mode RRL in all the dSphs apart from Sagittarius are completely lacking in High Amplitude Short Period (HASP) variables, defined as those having P lsim 0.48 days and AV >= 0.75 mag. Such variables are not uncommon in the Halo and among the globular clusters and massive dwarf irregulars. To further interpret this evidence, we considered 18 globulars covering a broad range in metallicity (–2.3 lsim [Fe/H] lsim –1.1) and hosting more than 35 RRL each. The metallicity turns out to be the main parameter, since only globulars more metal-rich than [Fe/H] ~ –1.5 host RRL in the HASP region. This finding suggests that dSphs similar to the surviving ones do not appear to be the major building-blocks of the Halo. Leading physical arguments suggest an extreme upper limit of ~50% to their contribution. On the other hand, massive dwarfs hosting an old population with a broad metallicity distribution (Large Magellanic Cloud, Sagittarius) may have played a primary role in the formation of the Halo.