I give the First Order this much: before their superweapon was destroyed, they at least got to use it against a military target and effectively wipe out the heart of the Republic. That's more than either Death Star ever accomplished against the Alliance.
I'm not going to compare their destruction of the New Republic of course to Palpatine's destruction of the Old Republic, as the First Order took out a governmental body only 30-something years old wheres Sidious meticulously dismantled one which was many thousands of years old. But giving the First Order the win on the superweapon side of things is more than fair.