We present radio and X-ray observations of the nearby Type IIb Supernova 2013df in NGC 4414 from 10 to 250 days after the explosion . The radio emission showed a peculiar soft-to-hard spectral evolution . We present a model in which inverse Compton cooling of synchrotron emitting electrons can account for the observed spectral and light curve evolution . A significant mass-loss rate , \dot { M } \approx 8 \times 10 ^ { -5 } M _ { \odot } /yr for a wind velocity of 10 km/s , is estimated from the detailed modeling of radio and X-ray emission , which are primarily due to synchrotron and bremsstrahlung , respectively . We show that SN 2013df is similar to SN 1993J in various ways . The shock wave speed of SN 2013df was found to be average among the radio supernovae ; v _ { sh } / c \sim 0.07 . We did not find any significant deviation from smooth decline in the light curve of SN 2013df . One of the main results of our self-consistent multiband modeling is the significant deviation from energy equipartition between magnetic fields and relativistic electrons behind the shock . We estimate \epsilon _ { e } = 200 \epsilon _ { B } . In general for Type IIb SNe , we find that the presence of bright optical cooling envelope emission is linked with free-free radio absorption and bright thermal X-ray emission . This finding suggests that more extended progenitors , similar to that of SN 2013df , suffer from substantial mass loss in the years before the supernova .