For all practical purposes the browser can only display the new UI.* I would guess the browser is lighter on resources but I haven’t done tests to prove it.
*Yes, the old Epicor web access exists, but it worked so badly and so limited that it might as well not exist.
If you don’t install the client at the workstation, you will not be able to use the Classic interface (or the Modern Shell interface, Epicor is now lumping them both into “Classic”).
If all they have is a browser, then all they have is Kinetic.