As a person coming from the data industry, I've dealt with exactly this situation.
Generally speaking, MySQL will be faster.
However, you don't state the type of application that you are developing. Are you developing a data warehouse application that is mainly used for searching and retrieval of records? How many fields are typically present in your records? How many records are typically present in your data files? Do these files have any relational properties to each other, i.e. do you have a file of customers and a file of customer orders? How much time do you have to develop a system?
The answer will depend on the answer to the questions listed previously. However, you can generally use the following as a guidelines:
If you are building a data warehouse application with records exceeding one million, you may want to consider ditching both and moving to a Column Oriented Database.
CSV will probably be faster for smaller data sets. However, rolling your own insert routines in CSV could be painful and you lose the advantages of database indexing.
My general recommendation would be to just use MySql, as I said previously, in most cases it will be faster.