We analyse in terms of efficiency and traction capabilities a recently patented traction drive, referred to as the double roller full-toroidal variator (DFTV). We compare its performance with the single roller full-toroidal variator (SFTV) and the single roller half-toroidal variator (SHTV). Modeling of these variators involves challenging tribological issues; the traction and efficiency performances depend on tribological phenomena occurring at the interface between rollers and disks, where the lubricant undergoes very severe elastohydrodynamic lubrication regimes. Interestingly, the DFTV shows an improvement of the mechanical efficiency over a wide range of transmission ratios and in particular at the unit speed ratio as in such conditions in which the DFTV allows for zero-spin, thus strongly enhancing its traction capabilities. The very high mechanical efficiency and traction performances of the DFTV are exploited to investigate the performance of a flywheel-based Kinetic Energy Recovery System (KERS), where the efficiency of the variator plays an important role in determining the overall energy recovery performance. The energy boost capabilities and the round-trip efficiency are calculated for the three different variators considered in this study. The results suggest that the energy recovery potential of the mechanical KERS can be improved with a proper choice of the variator.