Oracle Joins - Comparison between conventional syntax VS ANSI Syntax

In 11g you should be using ANSI join syntax. It is more flexible (support for full outer joins and partitioned joins), and as the documentation states:

Oracle strongly recommends that you use the more flexible FROM clause join syntax shown in the former example.

That's reason enough.

Grouping answers together

1. 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.
2. 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
3. SQL will not start to perform better after migration to ANSI syntax - it's just different syntax.
4. 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.
5. 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.
6. 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.
7. Oracle internally converts ANSI syntax to the (+) syntax, you can see this happening in the execution plan's Predicate Information section.

Possible Pitfall in using ANSI syntax on 12c engine

Including a possibility of bug in JOIN in 12c. See here

FOLLOW UP:

Quest SQL optimizer tool rewrites the SQL to ANSI syntax.

If your 200+ packages work as intended with "old fashioned" syntax, let it be. SQL will not start to perform better after migration to ANSI syntax - it's just different syntax.

All that being said, ANSI syntax is cleaner - you are not going to normal join if you forget (+) in some multi-column outer join.
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.
Of course, you know your environment and priorities better - as SchmitzIT said - ANSI syntax is part of SQL standard and it would help when going to use some other RDBMS product.