Function Looping Over Multiple Dataframes to Create New Categorical Data Column

There's ways to do such things in pandas:

def del_cat_migration(row):
    if row[0] == row[1]:
        return f"Same - {row[0]}"
    
    return f"{row[0]} to {row[1]}"

df3 = pd.concat([df1["Del_Cat"], df2["Del_Cat"]], axis=1)

df3 looks like

   Del_Cat  Del_Cat
0  Current  Current
1  Current    31-60
2    61-90    61-90
3    61-90  Current
4  Current    31-60

Now apply the function, row-wise (axis=1):

>>> df3.apply(del_cat_migration, axis=1)
0      Same - Current
1    Current to 31-60
2        Same - 61-90
3    61-90 to Current
4    Current to 31-60

The cause: you cannot do the comparison in if statement between two columns of a dataframe because the result of this comparison is a boolean series [True, False, ....] which is invalid condition, therefore, you should use a.empty, a.bool(), a.item(), a.any() or a.all() as indicated by the error log. The suggested option is invalid because you need only to compare between each entry in df1 and the corresponding entry in df2. I fixed this issue as in the solution below and also correct some syntax errors in the function.

But again, your function will have a problem with df2.apply() will iterate through each row and call the function in each row with the entire dataframes which is not valid operation, as well.

def del_cat_migration(df1, df2):
    bool_index = (df1['Loan Code/Number'] == df2['Loan Code/Number'])
    
    for i in df1.index[bool_index]:
        if (df1.loc[i,'Del_Cat'] == 'Current') & (df2.loc[i,'Del_Cat'] == 'Current'):
        df2.loc[i,'Del_Migration_Cat'] = 'Same - Current'
    elif (df1.loc[i,'Del_Cat'] == 'Current') & (df2.loc[i,'Del_Cat'] == '31-60'):
        df2.loc[i,'Del_Migration_Cat'] = 'Current to 31-60'
    elif (df1.loc[i,'Del_Cat'] == '31-60') & (df2.loc[i,'Del_Cat']  == '31-60'):
        df2.loc[i,'Del_Migration_Cat'] = 'Same - 31-60'
    elif (df1.loc[i,'Del_Cat'] == '31-60') & (df2.loc[i,'Del_Cat'] == '61-90'):
        df2.loc[i,'Del_Migration_Cat'] = '31-60 to 61-90'
    elif (df1.loc[i,'Del_Cat'] == '61-90') & (df2.loc[i,'Del_Cat'] == '61-90'):
        df2.loc[i,'Del_Migration_Cat'] = 'Same - 61-90'
    elif (df1.loc[i,'Del_Cat'] == '61-90') & (df2.loc[i,'Del_Cat']  == 'Current'):
        df2.loc[i,'Del_Migration_Cat'] = '61-90 to Current'
    else:
        df2.loc[i,'Del_Migration_Cat'] = 'Other'

del_cat_migration(df1, df2)

But I prefer to follow the answer of @fsimonjetz, however, you need for an extra dataframe df3.

first, let's merge df's on 'Loan Code/Number' column, then we can apply function:

df3 = pd.merge(df1, df2[['Loan Code/Number','Del_Cat']], 
               on='Loan Code/Number',
               how='left',
               suffixes=(None, '_2'))
print(df3)
'''
   Loan Code/Number  Days Delinquent  Del_Cat Del_Cat_2
0        1147623994              -25  Current   Current
1        1501719058               -5  Current       NaN
2        1501719696               77    61-90     61-90
3        1502624989               87    61-90       NaN
4        1502625152               16  Current     31-60
'''
df3 = (df3.assign(Del_Cat=df3.apply(lambda x: f"same {x['Del_Cat']}" 
                                    if x['Del_Cat']==x['Del_Cat_2'] 
                                    else 'Other' if x['Del_Cat_2']!=x['Del_Cat_2']
                                    else f"{x['Del_Cat']} to {x['Del_Cat_2']}", axis=1)).
       drop(columns='Del_Cat_2'))
print(df3)
'''
   Loan Code/Number  Days Delinquent           Del_Cat
0        1147623994              -25      same Current
1        1501719058               -5             Other
2        1501719696               77        same 61-90
3        1502624989               87             Other
4        1502625152               16  Current to 31-60