Groundspeak LiveAPI versus Geocaching.com website
The Groundspeak LiveAPI account uses the LiveAPI to access the data on the geocaching.com website. You can only use this account if you provide your own access keys.
The Geocaching.com website account uses some screen scraping and smart URL juggling to obtain the data required. It currently supports most of the features of the LiveAPI except trackables.
Which one to use
If you have a Groundspeak LiveAPI key, you should use the Groundspeak LiveAPI. However, Groundspeak doesn't release them anymore so the Geocube project cannot apply for them.
If you don't have a Groundspeak LiveAPI key, you should use the Geocaching.com website.
Will things break?
Yups. Unlike the Groundspeak LiveAPI which is properly defined and pretty static, the screen scraping and URL juggling will might fail when Groundspeak makes changes to the geocaching.com website. While everything is done to make sure that it doesn't fail dramatically, it might happen. Don't panic, please contact me and I'll fix it!