Extensively discussed many a times, including one by me.
Use explicit JOINs rather than implicit (regardless whether they are outer joins or not) is that it's much easier to accidently create a cartesian product with the implicit joins.
With explicit JOINs you cannot "by accident" create one. The more tables are involved the higher the risk is that you miss one join condition.
Basically (+) is severely limited compared to ANSI joins. Furthermore it is only available in Oracle whereas the ANSI join syntax is supported by all major DBMS
SQL will not start to perform better after migration to ANSI syntax - it's just different syntax.
Oracle strongly recommends that you use the more flexible FROM clause join syntax shown in the former example. In the past there were some bugs with ANSI syntax but if you go with latest 11.2 or 12.1 that should be fixed already.
Using the JOIN operators ensure your SQL code is ANSI compliant, and thus would allow a front-end application to be more easily ported for other database platforms.
Join conditions have a very low selectivity on each table and a high selectivity on the tuples in the theoretical cross product. Conditions in the where statement usually have a much higher selectivity.
Oracle internally converts ANSI syntax to the (+) syntax, you can see this happening in the execution plan's Predicate Information section.
If you are using 11.2 I advise ANSI join. If you use 12C, there are some new bugs unearthed on OUTER JOINS.
I also remember some bugs in Oracle while using ANSI syntax, before 11.2 where it got fixed in 11.2.
In my opinion, I am not a big fan of ANSI syntax, though Oracle does confirm to the standards of ANSI, it is not totally bug free.