We present a statistical analysis of the first 300 stars observed by the Gemini Planet Imager Exoplanet Survey. This subsample includes six detected planets and three brown dwarfs; from these detections and our contrast curves we infer the underlying distributions of substellar companions with respect to their mass, semimajor axis, and host stellar mass. We uncover a strong correlation between planet occurrence rate and host star mass, with stars M* > 1.5 M more likely to host planets with masses between 2 and 13MJup and semimajor axes of 3-100 au at 99.92% confidence. We fit a double power-law model in planet mass (m) and semimajor axis (a) for planet populations around high-mass stars (M* > 1.5 M ) of the form , finding = −2.4 0.8 and β = −2.0 0.5, and an integrated occurrence rate of % between 5-13MJup and 10-100 au. A significantly lower occurrence rate is obtained for brown dwarfs around all stars, with % of stars hosting a brown dwarf companion between 13-80MJup and 10-100 au. Brown dwarfs also appear to be distributed differently in mass and semimajor axis compared to giant planets; whereas giant planets follow a bottom-heavy mass distribution and favor smaller semimajor axes, brown dwarfs exhibit just the opposite behaviors. Comparing to studies of short-period giant planets from the radial velocity method, our results are consistent with a peak in occurrence of giant planets between ∼1 and 10 au. We discuss how these trends, including the preference of giant planets for high-mass host stars, point to formation of giant planets by core/pebble accretion, and formation of brown dwarfs by gravitational instability.