Sodium bicarbonate is also expected to give the desired product. But ammonium bicarbonate is advantageous as the ammonium salts form the products can easily be removed out

Please check whether your monodisperse MnCO3 synthesis is pH sensitive or not. The two bicarbonate salts should give slightly different pH values at a given concentration.

As mentioned by Bhattacharya, ammonium salts will definitely have the advantage in the removal stage, compared to sodium salt. 

you can use if you can easily separate the liquor at crystallization stage to remove sodium salts by any technique.