We present a census of ionized gas outflows in 599 normal galaxies at redshift 0.6<z<2.7, mostly based on integral field spectroscopy of Ha, [NII], and [SII] line emission. The sample fairly homogeneously covers the main sequence of star-forming galaxies with masses 9.0<log(M*/Msun)<11.7, and probes into the regimes of quiescent galaxies and starburst outliers. About 1/3 exhibits the high-velocity component indicative of outflows, roughly equally split into winds driven by star formation (SF) and active galactic nuclei (AGN). The incidence of SF-driven winds correlates mainly with star formation properties. These outflows have typical velocities of ~450 km/s, local electron densities of n_e~380 cm^-3, modest mass loading factors of ~0.1-0.2 at all galaxy masses, and energetics compatible with momentum driving by young stellar populations. The SF-driven winds may escape from log(M*/Msun)<10.3 galaxies but substantial mass, momentum, and energy in hotter and colder outflow phases seem required to account for low galaxy formation efficiencies in the low-mass regime. Faster AGN-driven outflows (~1000-2000 km/s) are commonly detected above log(M*/Msun)~10.7, in up to ~75% of log(M*/Msun)>11.2 galaxies. The incidence, strength, and velocity of AGN-driven winds strongly correlates with stellar mass and central concentration. Their outflowing ionized gas appears denser (n_e~1000 cm^-3), and possibly compressed and shock-excited. These winds have comparable mass loading factors as the SF-driven winds but carry ~10 (~50) times more momentum (energy). The results confirm our previous findings of high duty cycle, energy-driven outflows powered by AGN above the Schechter mass, which may contribute to star formation quenching.