In SQL, this problem could be solved by several methods:
select * from df1 where exists (select * from df2 where df2.user_id = df1.user_id)
union all
select * from df2 where exists (select * from df1 where df1.user_id = df2.user_id)
or join and then unpivot (possible in SQL server)
select
df1.user_id,
c.rating
from df1
inner join df2 on df2.user_i = df1.user_id
outer apply (
select df1.rating union all
select df2.rating
) as c
Second one could be written in pandas with something like:
>>> df1 = pd.DataFrame({"user_id":[1,2,3], "rating":[10, 15, 20]})
>>> df2 = pd.DataFrame({"user_id":[3,4,5], "rating":[30, 35, 40]})
>>>
>>> df4 = df[['user_id', 'rating_1']].rename(columns={'rating_1':'rating'})
>>> df = pd.merge(df1, df2, on='user_id', suffixes=['_1', '_2'])
>>> df3 = df[['user_id', 'rating_1']].rename(columns={'rating_1':'rating'})
>>> df4 = df[['user_id', 'rating_2']].rename(columns={'rating_2':'rating'})
>>> pd.concat([df3, df4], axis=0)
user_id rating
0 3 20
0 3 30