I have to create a form with a fulltext search field and a dropdown listing every terms of a certain vocabulary. On submission the form is redirecting the user with the value of both the fields as parameters in path. I don't know which should be better to use between a facet or a simple list listing every terms of the needed vocabulary?
Facets are usually used for a lot more complex examples with many properties to narrow down your search by.
Both facets and the usual Views with Exposed filters form create paths that hold search parameters entered by users.
The simplest case would probably be to add the textual filter for the Body field, and the Filter for the Taxonomy reference field, and Expose them (so that the users can choose values for them and narrow down the search results). You can use Exposed form settings to change the way the form fields display, drop-downs sometimes aren't the most usable options.
You can use Better Exposed Filters module if you need more options for the exposed form display.