Assume you are in level trimmed forward flight in a conventional helicopter(one main rotor with an anti torque tail rotor).  Will a level coordinated turn to the left require more/less/equal power compared to a turn to the right?  Why?

More power in a UH-1E. The torque caused by the powering of the main rotor causes the airframe to yaw starboard, opposite main rotor rotation. To cause a yaw to port (as in turning to port) the tail rotor blades need to be increased in pitch. An increase of blade pitch in either rotor system during steady level flight requires an increase in power to maintain steady, level, flight.

What model? Which way does the main rotor turn?

I picked the model I knew.

P factor

Torque steer

A specific model of helicopter doesn't matter.  Big hint: rotor rotation direction changes the answer!

Run me through it...

At any given point the sum of the lift is equal to the weight of the helicopter, requiring the same vector for identical bank angles.  So, the total power required for the main rotor would be equal, in either direction (assuming equal bank turns).  (I'm assuming the same relative airflow over the blade...but might be wrong?)  Does the retreating blade being on the high or low side make a difference?  (Additionally, are we factoring the vector of the tail-rotor's lift component at the bank angle?  If the bank tilts the anti-torque up, then there is an additional lift component from the tail-rotor)

If it is in trim, the anti-torque required should be directly proportional to the total power required...which would be the same.

Now, rolling in and out of the turn, the transient torque will be greater rolling toward the retreating blade side...

We have a winner!
We're talking the whole aircraft, so of course the tail rotor counts.  
There's numerous small things that make a difference, but the direction of tail rotor thrust outweighs them all by a large margin.

So on helicopters with forward rotating blades (ie. U.S. helicopters, or with the advancing blade on the right side of the aircraft, CCW from above, etc) a level trimmed turn at a constant airspeed to the left requires less power than the same turn to the right.  When you bank left the tail rotor thrust vector is inclined and adds lift to the aircraft.  Conversly, when you turn right the tail rotor thrust is towards the ground, requiring a higher power setting to negate the downward thrust of the tail rotor.

This is commonly confused because it is opposite of power required at a hover - for a "right side forward" helicopter at a hover, a right yaw requires less power because you are reducing the tail rotor thrust.  This is often taught early on in flight training and pilots often incorrectly assume the same is true in forward flight.