First compare both DataFrames and get al least one Trues per rows by any and then use boolean indexing for filtering ssno column:
df1 = pd.DataFrame({'ssno':list('abcdef'),
'B':[4,5,4,5,5,4],
'C':[70,8,9,4,2,3],
'D':[1,3,5,7,1,0],
'E':[5,3,6,90,2,4],
'F':list('aaXbbb')})
print (df1)
B C D E F ssno
0 4 70 1 5 a a
1 5 8 3 3 a b
2 4 9 5 6 X c
3 5 4 7 90 b d
4 5 2 1 2 b e
5 4 3 0 4 b f
df2 = pd.DataFrame({'ssno':list('abcdef'),
'B':[4,5,4,5,5,4],
'C':[7,8,9,4,2,3],
'D':[1,3,5,7,1,0],
'E':[5,3,6,9,2,4],
'F':list('aaabbb')})
print (df2)
B C D E F ssno
0 4 7 1 5 a a
1 5 8 3 3 a b
2 4 9 5 6 a c
3 5 4 7 9 b d
4 5 2 1 2 b e
s = df1.loc[(df1 != df2).any(1), 'ssno']
print (s)
0 a
2 c
3 d
Name: ssno, dtype: object
Detail:
print (df1 != df2)
B C D E F ssno
0 False True False False False False
1 False False False False False False
2 False False False False True False
3 False False False True False False
4 False False False False False False
5 False False False False False False
print ((df1 != df2).any(1))
0 True
1 False
2 True
3 True
4 False
5 False
dtype: bool