Chase lets you choose the file extension if you manually download the data. It doesn't matter if you use Quicken, too. You can do both.
If you use "DirectConnect" then the download happens from within QuickBooks itself (and/or Quicken itself). You don't need to open the chase.com web site to access the data. In that case you can also download the data to both QuickBooks and Quicken - the determination of which "file type" is done automatically.