  We theoretically study collisions between ultracold polar molecules that are
polarized by microwave or static electric fields. We systematically study the
dependence on field strength, microwave polarization, and detuning from
rotational transitions. We calculate the loss in two-body collisions that is
observable experimentally and compare to the results expected for purely
first-order dipolar interactions. For ground state molecules polarized by a
static electric field, the dynamics are accurately described by first-order
dipolar interactions. For microwave dressing, instead, resonant dipolar
collisions dominate the collision process, in which molecules reorient along
the intermolecular axis and interact with the full strength of the transition
dipole. For red detuning, reorientation can only be suppressed at extreme Rabi
frequencies. For blue detuned microwaves, resonant dipolar interactions
dominate even for high Rabi frequencies, leading to microwave shielding for
circular polarization and structured losses due to resonances for linear
polarization. The results are presented numerically for fermionic
$^{23}$Na$^{40}$K and bosonic $^{23}$Na$^{39}$K molecules.
