Oracle <> , != , ^= operators

Question

I want to know the difference of those operators, mainly their performance difference.

I have had a look at Difference between <> and != in SQL, it has no performance related information.

Then I found this on dba-oracle.com, it suggests that in 10.2 onwards the performance can be quite different.

I wonder why? does != always perform better then <>?

NOTE: Our tests, and performance on the live system shows, changing from <> to != has a big impact on the time the queries return in. I am here to ask WHY this is happening, not whether they are same or not. I know semantically they are, but in reality they are different.