We present measurements of the dissipative turbulent drag on a vibrating grid in superfluid ⁴He over a wide range of (low) frequencies. At high velocities, the dissipative drag is independent of frequency and is approximately the same as that measured in normal liquid ⁴He. We present measurements on a similar grid in superfluid ³He-B at low temperatures which shows an almost identical turbulent drag coefficient at low frequencies. However, the turbulent drag in ³He-B is substantially higher at higher frequencies. We also present measurements of the inertial drag coefficient for grid turbulence in ⁴He. The inertial drag coefficient is significantly reduced by turbulence in both superfluid and normal liquid ⁴He.