gdb: garmin proprietary gps info database format (but it has been reverse engineered) invented for use in mapsource.
gpx: open format (an xml schema) invented by topographics, I think, used for vender agnostic gps data interchange. This format is now starting to be used by garmin.
The GPX 1.1 schema was released on August 9, 2004. GPX has been the de-facto XML standard for lightweight interchange of GPS data since the initial GPX 1.0 release in 2002. GPX is being used by dozens of software programs and Web services for GPS data exchange, mapping, and geocaching.
If you want your data usable in non-garmin devices or software then GPX is a safer choice. Also, you can look at (and edit!) a gpx file in a text editor. I sometimes do that to trim track logs downloaded from the gps in gpx format.