A DSN connection makes use of a system or file DSN (hence the name). These are convenient because if you need to change the settings you don’t have to do find the info in the config file looking for the connection string. You have a nice little wizard to walk you through making the changes to the DSN. The downside to the DSN is that you have to make sure that the DSN is setup correctly on each machine that you are installing the software on.
Using just a connection string is nice because it’s easier to find the connection string as it’s in the same place as all the other settings. With having the connection string within the config file you also have the ability to encrypt the connection string which you don’t have when using the DSN.