Cloud storage services should be favored especially in cases of distant collaboration or multi-site work. They are not acceptable for sensitive data, and specific informed consent is required to store any personal data on them.
Your @graduateinstitute.ch account gives you extended institutional access to Google Drive.
Your institutional account also includes a Team Drive. This specific kind of Google Drive can be used in the case of projects that should remain in control of the Institute: access can be managed by the IT service, which allows for ownership transfer, and it includes advanced file restoration tools.
Synchronisation applications can be installed on your computer and mobile devices. While they are efficient, Google Drive's synchronisation is considerably slower than Dropbox's.
G suite tools are also very interesting when collaborating with other researchers.
The Dropbox free account is much more limited than Google Drive's, but this service is extremely popular in academic circles. This means that it could be favored when collaborating with external researchers, even if it requires payment to become sufficient.
Another advantage of Dropbox over Google Drive is the speed of its synchronisation tool. It achieves much better results by using block-level transfer, which skips the parts of files which have not changed.
You may of course opt for other cloud storage services. The following solutions could be interesting: