Didger uses 3-parameter Molodensky (delta x,y,z,ellipsoid) to convert from NAD83 to NAD27. It looks like Global Mapper is not using the same 3-parameter conversion, but rather it is using an inverse NADCON method to convert from NAD83 to NAD27.
Didger currently doesn't support the inverse NADCON method. To add your vote to this request on the Didger suggestion file, please email your request to email@example.com.
Updated: October 5, 2016