Mixing of molecular cations enhances the optoelectronic properties and stability of hybrid lead halide perovskites. Here, we use a multitechnique approach to determine the phase diagram and molecular cation dynamics of mixed methylammonium-formamidinium MA1-xFAxPbBr3 (0 ≤ x ≤ 1) hybrid perovskites. The calorimetric, ultrasonic, and X-ray diffraction experiments show a substantial suppression of the structural phase transitions and stabilization of the cubic phase upon mixing. We use the broad-band dielectric and Raman spectroscopies to study the MA and FA cation dynamics in these compounds. The broad-band dielectric spectroscopy indicates the absence of the MA cation ordering and a gradual increase of the rotation barrier upon mixing. The room-temperature dielectric permittivity substantially decreases as the fraction of the FA cations is increased. No significant changes of the permittivity are detected at temperatures, where the dielectric relaxations are absent. We also observe weak signatures of a dipolar glass phase for the intermediate mixing levels. The Raman spectroscopy supports the dielectric results and reveals additional subtle information about the FA cation dynamics.