Unless you have huge volumes of traffic, it's unlikely to make much of a difference. If you do get huge volumes of traffic, some of the higher-end Oracle solutions will be excellent, if you have the money to invest into the software. The free Oracle XE is a low-to-medium range entry level solution.

In an application like this, and at the volumes most of us receive, it's more a question of how smart the database queries are written. If your application runs on well-optimized MySQL queries, and see more if you get low to medium traffic, it's unlikely your site will get noticeably faster with a different database software.

Then again, if you are running a very high-volume site, there are ways of further optimizing MySQL for heavy stress performance. You will have to have a huge site and rather particular needs to justify adopting a different database solution, given the extent of support MySQL enjoys in the current hosting environments.