Magnetic field of 2 solenoids
Figure 1. The right-hand rule for polarity of a solenoid. Source: Commons.

If you apply the right-hand rule twice, once for each direction of the current you will see that the result is zero flux. They cancel out. No inductance. No magnetic field.


  Which one gives the lower emf to nearby components (the best emf cancelling effect)?


Contra-currents will minimise EMF but gives you no inductance so it is no use.

All of this assumes that your winding direction is the same for both coils as shown in your diagram. If wound opposite rotation then the contra-current would end up adding to the first coil.

Note: I once had to create a 1 &Omega; test load for a 30 A current controller. We wound the right length of 1.5 mm2 insulated wire into a foot diameter coil. When powered with 50 Hz it would vibrate severely on the table top. We unwound it, folded it in half and rewound it. There was then no vibration from the coil. We had cancelled out any magnetic field almost completely.