Hemigrammus rhodostomus is the "true" rummy-nose tetra and is sometimes referred to as the "Banded Rummy-Nose." It is found closer to the Atlantic coastline. It is considered to be easier to breed than the other two rummy-nose tetras. It requires quite soft and acidic water. Hemigrammus bleheri may also be known as the "common" rummy-nose tetra or "Brilliant Rummy-Nose,". It is found farther inland than H. rhodostomus, and has a much narrower range, basically the middle portion of the Rio Negro in Brazil. Like the "true" rummy-nose tetra, the common rummy-nose requires quite soft and acidic water. Petitella georgiae is the "false" rummy-nose tetra, and may also be called the "Black-Finned Rummy-Nose." It is also found farther inland than H. rhodostomus, but its range is much broader than H. bleheri and includes Brazil and Peru. P. georgiae can live in water that is less acidic with more hardness (pH 5.5-7.0; hardness up to 8şKH).
Did I mention that I would keep any of the three ;-)