I've done something similar, using C# instead of Processing and SqlServer instead of MySQL (though those changes are trivial).
Storing the data in the database is better in terms of long term storage and the ability to perform trend analysis. If it is stored on the Arduino, you need to take the Arduino out of action to retrieve the SD card, to get its data.
Then, you still need to perform the analysis on the data, which will typically involve reformatting the data anyway.
Storing the data in a database can support automatic time stamping, meaning that there is one less thing that the Arduino needs to deal with (sending time/date information from a RTC).
I'm not sure that Processing can access MySQL directly, though it might be possible to develop a library to accomplish this. PHP certainly can.
PHP is ideal for developing web applications, so rather than having Processing do the visualization part, let the web browser to that.