I have also run into this issue. At first I set up a complex set of if/else statements to handle this but then someone recommended using a simple python dictionary to convert the reported type to the desired type.fieldTypeDictionary = {'SmallInteger': 'SHORT', 'Integer': 'LONG', 'Single': 'FLOAT', 'Double': 'DOUBLE', 'String': 'TEXT', 'Date': 'DATE'}
fldType = searchTheField.field_type
arcpy.AddField_management(updateDSParam,updateFieldParam,fieldTypeDictionary[fldType], fldPrecision, fldScale, fldLength)
I hope this helps, good luck.Joel