An absorbing layer of a low-E coating is designed to cause the coating to have a more neutral and/or green color at normal and/or certain off-axis viewing angles. In certain example embodiments, the metallic or substantially metallic absorbing layer (e.g., NiCr) is from about 20-30 angstroms (Å) thick; this thickness has been found to unexpectedly provide less red and more neutral coloration for the coated article at certain off-axis viewing angles (e.g., at a 45 degree off-axis viewing angle). In certain example embodiments, the absorbing layer is provided between first and second nitride layers in order to reduce or prevent oxidation thereof during heat treatment thereby permitting predictable coloration to be achieved following the heat treatment. Coated articles according to certain example embodiments of this invention may be used in the context of insulating glass (IG) window units, vehicle windows, other types of windows, or in any other suitable application.