We discuss the formation of the halo of M31 and the Milky Way as traced by the population of RR Lyrae stars, in comparison with the population of such stars preent in satellite dwarf galaxies. We find that both halos and the massive dwarf host a population of high amplitude short period RRab stars, absent in low-mass dwarfs. These stars are explained as the metal-rich tail of the RR Lyrae distribution ([Fe/H] ˜ - 1.5), and thus their existence imply fast chemical enrichment in the host system. Their presence in both halos implies that massive building blocks had an important role in their formation.