Technical:

GPX and TCX are both XML file formats. Both contain GPS waypoints, tracks, routes, etc.

GPX is an open format, free for development use without licenses.

TCX is a proprietary format developed by Garmin. It allows additional information such as heart beat and cadence.

IOW, unless you plan to use a non-Garmin device, it doesn't matter what format you use going from the website to your Garmin GPS device.