What's the relationship between DC braking torque and AC turning torque for a given current on a BLDC motor
With 6 step commutation only 2 terminals are powered at the same time, just like your constant DC current. The difference is that when running the controller powers different phases in sync with the rotor position to produce a relatively constant torque, whereas with constant DC current the torque alternates between positive and negative as the motor is rotated.

So at the same current both AC and DC produce the same peak torque, but with DC the average torque over a whole revolution is zero. 

Braking a BLDC motor with constant DC current would be just as effective as AC braking at the same current if the load wasn't strong enough to pull the rotor away from its maximum torque position (magnets directly in line with stator arms). But once the rotor starts moving the torque will reduce making it easier to rotate, reaching zero when the magnets are midway between stator arms and then assisting the load to rotate for the next half cycle. 

So a 'DC current brake' which was not strong enough to stop the motor from rotating would be very weak, because only friction and magnetic drag would be slowing it down.