Angular distributions have been measured for the (/sup 6/Li, /sup 6/He) reaction on targets of /sup 7/Li, /sup 12,14/C, /sup 26/Mg, and /sup 90/Zr at bombarding energies of 35, 25, and 14 MeV/nucleon. The ratios of observed cross sections for states in /sup 14/N and /sup 7/Be suggest that the reaction mechanism is predominantly one-step at 35 and 25 MeV/nucleon with an increasing contribution from sequential transfer at lower energies. Measured forward-angle cross sections for Gamow-Teller transitions are found to be accurately proportional to the corresponding B(GT) values from ..beta../sup -/ decay or from (p,n) data. This calibration will allow the measurement of spin-transfer strength with the (/sup 6/Li, /sup 6/He) reaction at intermediate energies. One-step distorted-wave Born approximation calculations, which used Yukawa central and r/sup 2/ x Yukawa tensor potentials, are consistent with the data at 35 and 25 MeV/nucleon except for theta/sub c.m./<3/sup 0/, and give a central force strength, V/sub sigma//sub tau/, in reasonable agreement with that obtained in (p,n) studies at similar energies per nucleon.