How to group and aggregate different dataframes in pandas

1. You can use pd.concat on the two grouped dataframes and pass axis=1 (This is essentailly an outer join with pd.merge, but the syntax is a bit more concise).
2. Then, just do some cleanup with .fillna(0), rename columns as desired with .rename() and use .astype(int) to make the columns data types integers:

df3 = (pd.concat([df1.groupby("A").size(), df2.groupby("A").size()], axis=1)
      .fillna(0).rename({0 : 'df1', 1 : 'df2'}, axis=1).astype(int))
df3
Out[1]: 
   df1  df2
a    3    2
b    2    0
c    0    2

If you're working in pandas I would do an outer join.

data = [['a','a','a','b','b'],[1,1,4,1,3]]
df1 = pd.DataFrame(data).T
df1.columns = ['A','B']

data = [['a','a','c','c'],[1,2,3,5]]
df2 = pd.DataFrame(data).T
df2.columns = ['A','B']

temp1 = pd.DataFrame(df1.groupby("A").size())
temp2 = pd.DataFrame(df2.groupby("A").size())

df = temp1.merge(temp2,how='outer',left_index=True,right_index=True)
df.fillna(0)

output

0_x 0_y
A       
a   3.0 2.0
b   2.0 0.0
c   0.0 2.0

In concat is possible use parameter keys for new column names, because working with Series, then replace missing values and convert to integers:

df3 = (pd.concat([df1.groupby("A").size(), 
                  df2.groupby("A").size()], axis=1, keys=['df1','df2'])
         .fillna(0)
         .astype(int))
print (df3)
   df1  df2
a    3    2
b    2    0
c    0    2

Another idea is first use concat, convert MultiIndex to columns by DataFrame.reset_index, so possible use DataFrame.pivot_table, last use DataFrame.rename_axis:

df3 = (pd.concat([df1, df2], keys=['df1','df2'])
         .reset_index()
         .pivot_table(index='A', columns='level_0', aggfunc='size', fill_value=0)
         .rename_axis(columns=None, index=None)
       )
print (df3)
   df1  df2
a    3    2
b    2    0
c    0    2

You can do the below:

In [883]: df1 = df1.groupby("A").size().reset_index()

In [884]: df2 = df2.groupby("A").size().reset_index()

In [886]: df1.merge(df2, on='A', how='outer').fillna(0).rename(columns={'0_x': 'df1', '0_y':'df2'}).set_index('A')
Out[886]: 
   df1  df2
A          
a  3.0  2.0
b  2.0  0.0
c  0.0  2.0

 #groupby using agg to rename axis.
   g=df1.groupby("A", as_index=False)['B'].agg({'df1':'size'})
    h=df2.groupby("A", as_index=False)['B'].agg({'df2':'size'})

#concat the resultant datframe, fffiil, bfill and dro duplicates

(pd.concat([g,h], ignore_index=True).sort_values(by='A').ffill().bfill()).drop_duplicates()



  A  df1  df2
0  a  3.0  2.0
1  b  2.0  2.0
3  c  2.0  2.0

Just a variant of @David's answer :

frames = {"df1": df1, "df2": df2}

pd.concat(
    {key: value.groupby("A").size() for key, value in frames.items()}, axis=1
).fillna(0)