This paper compares the features of second generation (2G) High Temperature Superconducting (HTS) field coil with those of magnesium diboride ($MgB_2$) field coil for a 10 MW class superconducting generator. Both coils can function effectively in their respective magnetic flux density range: 10-12 T for 2G HTS field coil, 2 T for $MgB_2$ superconducting field coil. Even though some leading researchers have been developing 10 MW class superconducting generator with 2G HTS field coil, other research groups have begun to focus on $MgB_2$ wire, which is more economical and suitable for mass production. However 2G HTS wire is still appealing in functions such as in-field property and critical temperature, it shows higher in-field property and critical temperature than $MgB_2$ wire.