the only "logical" explanation I have is that previously with the "DUD" battery, your alternator was under severe load trying to constantly keep the battery charged and supplying the demands of the electrical system.
that will cause extra load via the alternator belt on the engine, and to compensate the engine management would have supplied extra fuel to keep the engine RPM up to account for the extra "drag" that the overworked alternator was placing on the system.
Now with a new battery, the alternator has a much easier job keeping the voltage supply at its peak, meaning less load and thus less "drag" from the alternator on the engine, and hence an easier free idle.
I think you will notice the same effect when you switch the aircon "on", whilst idling, the drag from the aircon pump on the engine causes it to step up its idling speed to compensate for the increased load, turn the aircon "off" and the idle drops due to it being freed from the load of the aircon compressor.
