We present an in-depth study of the large-scale, western jet of the microquasar XTE J1550-564, based on X-ray and radio observations performed in 2002-2003. The jet is spatially resolved in both observing windows. The X-ray jet is expanding in time along the axis of the jets propagation: we observe the formation of a tail (~2.25), which appears to extend backwards with an apparent velocity ~-0.10c. The origin of this feature is discussed in the framework of scenarios of energy dissipation. A single power-law adequately describes the broadband spectra, supporting a synchrotron origin of the X-ray emission. However, a spectral break at ~10^{15} Hz is necessary in coincidence with a re-flare at 8.64 GHz in September 2002. This finding may be indicative of emission from newly accelerated low-energy particles. The first detection of the jet is in February 2001 (F_{8.64GHz}=0.25+/-0.09 mJy) in the flux rising phase. A phase of stable emission is followed by a rapid decay (t_{decay}=167+/-5 days). The decay at radio frequencies is significantly shorter than in X-rays (t_{decay}=338+/-14 days). We detected a high fraction (up to ~9%) of linearly polarized radiation at 4.8 GHz and 8.6 GHz. The orientation of the electric vector is consistent with the picture of a shock-compressed magnetic field, and there are hints of variations on month-timescales, possibly connected with the evolution of the jet structure.
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