We present a statistical analysis of the first 300 stars observed by the Gemini Planet Imager Exoplanet Survey (GPIES). 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, semi-major axis, and host stellar mass. We uncover a strong correlation between planet occurrence rate and host star mass, with stars M * > 1.5M more likely to host planets with masses between 2-13M Jup and semi-major axes of 3-100au at 99.92% confidence. We fit a double power-law model in planet mass (m) and semi-major axis (a) for planet populations around high-mass stars (M * > 1.5M ) of the form d 2 N/(dm da)∝m α a β , finding α = −2.4 ± 0.8 and β = −2.0 ± 0.5, and an integrated occurrence rate of 9 +5 −4 % between 5-13M Jup and 10-100au. A significantly lower occurrence rate is obtained for brown dwarfs around all stars, with 0.8 +0.8 −0.5 % of stars hosting a brown dwarf companion between 13-80M Jup and 10-100au. Brown dwarfs also appear to be distributed differently in mass and semi-major axis compared to giant planets; whereas giant planets follow a bottom-heavy mass distribution and favor smaller semi-major axes, brown dwarfs exhibit just the opposite behaviors. Comparing to studies of short-period giant planets from the RV method, our results are consistent with a peak in occurrence of giant planets between ∼1-10au. 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.