How do I find the common values in two different dataframe by comparing different column names?
You can use pandas.merge() to get the common rows based on the columns. Try this:

df3 = pd.merge(df1, df2, how='inner', left_on='UniqueID', right_on='ID')


However, this will give you all the columns. After that you can use 

df3.drop([column_names], inplace=True)


to drop the columns that are not required.