How can I map between two enums using Automapper?

Alternatively to writing custom converters, just use ConvertUsing()

Mapper.CreateMap<EnumSrc, EnumDst>().ConvertUsing((value, destination) => 
{
    switch(value)
    {
        case EnumSrc.Option1:
            return EnumDst.Choice1;
        case EnumSrc.Option2:
            return EnumDst.Choice2;
        case EnumSrc.Option3:
            return EnumDst.Choice3;
        default:
            return EnumDst.None;
    }
});

You don't need to do CreateMap for enum types. Just get rid of the CreateMap call and it should work, as long as the names and/or values match up between enum types.