If you want to check equal values on a certain column, let's say Name, you can merge both DataFrames to a new one:

mergedStuff = pd.merge(df1, df2, on=['Name'], how='inner')
mergedStuff.head()

I think this is more efficient and faster than where if you have a big data set.

Just do with simple merge follow with dropna

df2.merge(df1,how='left').dropna().drop('Security',1)
Out[318]: 
  userID  ID   Sex  Date  Month  Year
4   John  45  Male    31      3  1975
5    Tom  22  Male     1      1  1990
7   Hary  56  Male    15      9  1970

import pandas as pd
import numpy as np

old = pd.DataFrame({
    "ID": ["AA", "BB", "CC"],
    "Rating": ["High", "Low", "Medium"],
    "Status": ["On track", "Monitor", "On track"]
})

new = pd.DataFrame({
    "ID": ["AA", "BB", "CC", "DD"],
    "Rating": ["Medium", "High", "Medium", "Low"],
    "Status": ["On track", "On track", "On track", "Monitor"]
})

(
    old
    # join the two dataframes used the ID column as a key
    .merge(new, how="outer", on="ID", suffixes=("_old", "_new"))
    # compare columns between old and new dataframe and assign new values
    .assign(
        Rating = lambda x: np.select(
            [x["Rating_new"].notna() & x["Rating_old"].isna(), x["Rating_new"] != x["Rating_old"]],
            ["New", "From '" + x["Rating_old"] +  "' To '" + x["Rating_new"] + "'"],
            default=np.nan
        ),
        Status = lambda x: np.select(
            [x["Status_new"].notna() & x["Status_old"].isna(), x["Status_new"] != x["Status_old"]],
            ["New", "From '" + x["Status_old"] +  "' To '" + x["Status_new"] + "'"],
            default=np.nan
        )
    )
    # select final columns
    .loc[:, ["ID", "Rating", "Status"]]
)

The first part is similar to Constantine, you can get the boolean of which rows are empty*:

In [21]: ne = (df1 != df2).any(1)

In [22]: ne
Out[22]:
0    False
1     True
2     True
dtype: bool

Then we can see which entries have changed:

In [23]: ne_stacked = (df1 != df2).stack()

In [24]: changed = ne_stacked[ne_stacked]

In [25]: changed.index.names = ['id', 'col']

In [26]: changed
Out[26]:
id  col
1   score         True
2   isEnrolled    True
    Comment       True
dtype: bool

Here the first entry is the index and the second the columns which has been changed.

In [27]: difference_locations = np.where(df1 != df2)

In [28]: changed_from = df1.values[difference_locations]

In [29]: changed_to = df2.values[difference_locations]

In [30]: pd.DataFrame({'from': changed_from, 'to': changed_to}, index=changed.index)
Out[30]:
               from           to
id col
1  score       1.11         1.21
2  isEnrolled  True        False
   Comment     None  On vacation

* Note: it's important that df1 and df2 share the same index here. To overcome this ambiguity, you can ensure you only look at the shared labels using df1.index & df2.index, but I think I'll leave that as an exercise.