I don't really like that this is named DB_eXist. People could easily think that this is a driver for the DB package. Then again, I can think of no better alternatives right now.
Why use defines for the output modes? Why not just use the straight strings? The strings are far shorter than the defines.
PEAR packages shouldn't be checking for PHP version runtime, the installer takes care of this. (In addition, defining it right before you use it is pretty worthless.)
PEAR packages may not die().
Classnames are incorrect. See the naming documents. Drivers should probably be e.g. DB_Exist_Driver and the class file must be DB/Exist/Driver.php.
Don't use paths relative to __FILE__ to include files, includ relative to the PEAR install dir (i.e. from the include_path).
Use lower-case null.
It would make more sense to me to allow the WSDL URLs to be set in the constructor.
Exceptions thrown must be a sub-class of PEAR_Exception nammed after your package. So DB_Exist_Exception.
is_readable() does not take into account the include_path so you can't use it as-is. I suggest something like the includeClass function in this class: