SQL INNER JOIN syntax

Actually these examples are equivalent and neither is a cartesian product. A cartesian product is returned when you join two tables without specifying a join condition, such as in

select *
from t1,t2

There is a good discussion of this on Wikipedia.

Both queries are an inner joins and equivalent. The first is the older method of doing things, whereas the use of the JOIN syntax only became common after the introduction of the SQL-92 standard (I believe it's in the older definitions, just wasn't particularly widely used before then).

The use of the JOIN syntax is strongly preferred as it separates the join logic from the filtering logic in the WHERE clause. Whilst the JOIN syntax is really syntactic sugar for inner joins it's strength lies with outer joins where the old * syntax can produce situations where it is impossible to unambiguously describe the join and the interpretation is implementation-dependent. The [LEFT | RIGHT] JOIN syntax avoids these pitfalls, and hence for consistency the use of the JOIN clause is preferable in all circumstances.

Note that neither of these two examples are Cartesian products. For that you'd use either

SELECT c.name, o.product  
FROM customer c, order o  
WHERE o.value = 150  

or

SELECT c.name, o.product  
FROM customer c  CROSS JOIN order o 
WHERE o.value = 150

To answer part of your question, I think early bugs in the JOIN ... ON syntax in Oracle discouraged Oracle users away from that syntax. I don't think there are any particular problems now.

They are equivalent and should be parsed into the same internal representation for optimization.

Oracle was late in supporting the JOIN ... ON (ANSI) syntax (not until Oracle 9), that's why Oracle developers often don't use it.

Personally, I prefer using ANSI syntax when it is logically clear that one table is driving the query and the others are lookup tables. When tables are "equal", I tend to use the cartesian syntax.

The performance should not differ at all.