Binding energies of negative (X − ) and positive trions (X + ) in quantum wires are studied for strong quantum confinement of carriers which results in a numerical exactly solvable model. The relative electron and hole localization has a strong effect on the stability of trions. For equal hole and electron confinement, X + is more stable but a small imbalance of the particle localization towards a stronger hole localization e.g. due to its larger effective mass, leads to the interchange of X − and X + recombination lines in the photoluminescent spectrum as was recently observed experimentally. In case of larger X − stability, a magnetic field oriented parallel to the wire axis leads to a stronger increase of the X + binding energy resulting in a crossing of the X + and X − lines.