If you can't SA every turn at your table (and you certainly can't at mine) then it is not better. If you can do SA every round a ranged Rogue will do more than a Barbarian at most levels. You mention brutal critical, this will illustrate the difference - the Barbarian gets brutal critical at 9th level which is an extra 1d12 (6.5) on a critical hit. At 9th level a Rogue with a Rapier or a crossbow does an extra 5d6 on a critical (17.5). So a Rogue has a critical that is nearly 3 times as damaging as brutal critical.but even without the 1 and 1/5 str...its still more than what a melee rogue can do (sorry, i didnt consider ranged with shapeshifter) and if it gets the racial feats of half orc or EA + rackless attack as an half elf, with brutal critical it can deal tons of damage. Anyway 5e I think is archery friendly and mostly of what you can do with a sword you can do it better with a bow (archery fighters, better if battlemaster, are awesome in 5e), but i would not understimate the dpr of a barbarian zealot, with the right race and the right feats i dont think is below the rogue, except sneak attack enter every round or to get a missunderstand about the surprised rules if we talk about assassin.
If you are concerned only about damage on a Rogue then ranged is best the way to go. But on a melee Rogue if you want to optimize damage you would take charger feat which would give you +5 damage if you move 10ft in a straight line. If you have a whip this is easy to do ....although you need to get proficiency in whip which a Rogue does not have automatically. If you do not have a whip you have to move a lot and take a lot of opportunity attacks to make it work but if you can handle the opportunity attacks you will do a lot of damage, at most levels more than a comparable barbarian. If you do not have a whip I would also get mobile feat if I wanted to do this. Every turn you need to back up, then take dash action and move10ft (3 meters) in a straight line toward the enemy and you get a bonus action attack with +5 damage.