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 perf
A Programmer will use !=
A DBA will use <>
If there is a different execution plan it may be that there are differences in the query cache or statistics for each notation. But I don't really think it is so.
Edit:
What I mean above. In complex databases there can be some strange side effects. I don't know oracle good enough, but I think there is an Query Compilation Cache like in SQL Server 2008 R2. If a query is compiled as new query, the database optimiser calculates a new execution plan depending on the current statistics. If the statistics has changed it will result in a other, may be a worse plan.