e_QUERY are URL parameters, so they are visible. With SEF-URL it is a bit complicated but it is still used.
With GET you need to know keys names. So it depends on your preferences. You can search closed issues for e_QUERY on e107 repo to get more information.
e107 is managing e_QUERY for you, you can rely on it. GET can surprise you :). Or I just don't have enough information how to set e_url addon to get all needed parameters as $_GET fields.
It is similar to e_PAGE vs e_ROUTE (new in 2.3.1). e_PAGE still works but with SEF-URL and e107 routing, it is safe to use e_ROUTE.