One important detail to notice is that your data has duplicate index values, so to perform any straightforward comparison we need to turn everything as unique with df.reset_index()
and therefore we can perform selections based on conditions. Once in your case the index is defined, I assume that you would like to keep de index so there are a one-line solution:
[~df2.reset_index().isin(df1.reset_index())].dropna().set_index('Date')
Once the objective from a pythonic perspective is to improve readability, we can break a little bit:
# keep the index name, if it does not have a name it uses the default name
index_name = df.index.name if df.index.name else 'index'
# setting the index to become unique
df1 = df1.reset_index()
df2 = df2.reset_index()
# getting the differences to a Dataframe
df_diff = df2[~df2.isin(df1)].dropna().set_index(index_name)