Have you looked at setting up a test system to determine if stats will help. You could setup up a system from an import. If you want to gen stats without effecting the optimizer change the optimizer_mode to rule.

Whether or not cbo or rule is faster depends on a lot of factors including: version of Oracle including which patches are installed, how you generate stats, how the tables are layed out in your database and what kinds of hints if any you use. Setting up a test system is the only way to know for certain without effecting your prod db's performance.