Well. The join is equivalent. i.e. they will return the same rows.

But if you use a select *, they will return the columns in a different order!

create table t1 as
  select rownum x from dual connect by level <= 2;
create table t2 as
  select rownum+1 x from dual connect by level <= 2;

select * from t1
left join t2
on   t1.x = t2.x;

X  X  
2  2  
1
 
select * from t2
right join t1
on   t1.x = t2.x;

X  X  
2  2  
   1

So strictly speaking they're not identical. To avoid this, explicitly specify the columns. Then you get the same output:

select t1.x, t2.x from t1
left join t2
on   t1.x = t2.x;

X  X  
2  2  
1
 
select t1.x, t2.x from t2
right join t1
on   t1.x = t2.x;

X  X  
2  2  
1

Do this and in both cases Oracle transforms the SQL to the following before executing it (run a 10053 trace to get this):

SELECT "T1"."X" "X","T2"."X" "X" 
FROM "CHRIS"."T1" "T1","CHRIS"."T2" "T2" 
WHERE "T1"."X"="T2"."X"(+);

Thus confirming they are "the same".