In terms of performance, I don't have any specific numbers.
Please elaborate on specific concerns you might have.
In general, with JPA you have far less control when it comes to performance tuning than you would if implementing a custom solution. However, JPA provides a solid, proven infrastructure with a boat load of functionality that you don't have to write yourself! JPA will definitely help you to more quickly get your application off the ground.
In terms of learning curve. If I assume you are starting fresh... there is a great deal to learn with either approach. Both require a working knowledge of SQL and entity relationship models. The JPA approach requires you learn JPA! Go figure! A MySQL approach requires knowledge of JDBC.
Your question, 'do stored procedure run faster than JPA queries' is not really the right question to ask. JPA 2.1 supports stored procedures. The better question would be, does a query in JPA run faster than a JDBC invoked MySQL query or does a stored procedure in JPA run faster than a JDBC invoked MYSQL stored procedure. All in all, a direct JDBC approach may be a bit faster than JPA, but only due to the small overhead of translating JPQL (JPA's SQL-like language) to SQL.