The real performance in sessions is that PHP overwrites the session data for each request. Writing to disk (which it will do in most cases) is very slow. It should only be used for simple things like authentication and small data structures, for example. shopping carts, etc.
Depending on what data and what software you have on the server, you must store it in a database or use a NoSQL solution such as MongoDB, Redis or CouchDB.
Since you are considering using sessions first, I believe data consistency is not number one priority. If the data is important, you should use the MySQL database, as it follows ACID principles and will store your data even after the client breaks itself into the current session.
If consistency is not important, consider using Memcached, if available.
Summary Use a database, but not necessarily MySQL (depending on what data it is).
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