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First light of the VLT planet finder SPHERE. II. The physical properties and the architecture of the young systems PZ Tel and HD 1160 revisited

[Abridged] Context. The young systems PZ Tel and HD 1160, hosting known low-mass companions, were observed during the commissioning of the new planet finder SPHERE with several imaging and spectroscopic modes. Aims. We aim to refine the physical properties and architecture of both systems. Methods. We use SPHERE commissioning data and REM observations, as well as literature and unpublished data from VLT/SINFONI, VLT/NaCo, Gemini/NICI, and Keck/NIRC2. Results. We derive new photometry and confirm the nearly daily photometric variability of PZ Tel A. Using literature data spanning 38 yr, we show that the star also exhibits a long-term variability trend. The 0.63-3.8 mic SED of PZ Tel B allows us to revise its properties: spectral type M7+/-1, Teff=2700+/-100 K, log(g)<4.5 dex, log(L/L_Sun)=-2.51+/-0.10 dex, and mass 38-72 MJ. The 1-3.8 mic SED of HD 1160 B suggests a massive brown dwarf or a low-mass star with spectral type M5.5-7.0, Teff=3000+/-100 K, [M/H]=-0.5-0.0 dex, log(L/L_Sun)=-2.81+/-0.10 dex, and mass 39-168 MJ. We confirm the deceleration and high eccentricity (e>0.66) of PZ Tel B. For e<0.9, the inclination, longitude of the ascending node, and time of periastron passage are well constrained. The system is seen close to an edge-on geometry. We reject other brown dwarf candidates outside 0.25" for both systems, and massive giant planets (>4 MJ) outside 0.5" for the PZ Tel system. We also show that K1-K2 color can be used with YJH low-resolution spectra to identify young L-type companions, provided high photometric accuracy (<0.05 mag) is achieved. Conclusions. SPHERE opens new horizons in the study of young brown dwarfs and giant exoplanets thanks to high-contrast imaging capabilities at optical and near-infrared wavelengths, as well as high signal-to-noise spectroscopy in the near-infrared from low (R~30-50) to medium resolutions (R~350).