Level 5 Rogue. 1 attack (rapier) at +7 dealing 3d6+1d8+4 [19] damage (presuming adjacent PC to trigger sneak attack) = around 19 damage.
Level 5 Paladin. 2 attacks (Greatsword) at +7 dealing 4d6+8 damage -re'roll 1s and 2s = around 25 damage.
The smart rogue uses dual shortswords in melee rather than a rapier unless they're going Arcane Trickster and need the off-hand for spellcasting components. That's 5d6+4 damage, for around 21.5 damage per round - still not as much as the paladin can dish out, but it's pretty close. The paladin also loses half that damage (for around 12.5) if he misses one attack, whereas the rogue only loses 1d6 (for around 18 damage). Heck, if the rouge lands the first hit, they can spend their bonus action on one of their Cunning Action options instead of blowing it on a chance at a few extra points of damage. Even assuming the paladin does land both hits and the rogue lands the first one and Disengages or something, that's a tradeoff of 7 DPR, 2 AC, and -4-5 athletics for 1,455 gold, +4-5 Initiative, +4-5 stealth and no disadvantage, +4-5 acrobatics, +4-5 sleight of hand, +4-5 thieves's tools
all before proficiency/expertise. I'd say the paladin's getting the raw end of the deal here.
The Paladin also has roughly 6 x smites and/or smite spells, 3 x divine channels (including either +Cha to hit and damage or advantage to hit), and damage buffs from +1d4 radiant to every hit, or Hunters mark from V-Pal.
Sure, but the Paladin still gets all of that if they go Dex instead of Str, which is IMO the smarter choice.
No feats here, but if allowed, there is better feat support for the Greatsword (GWM's power attack and cleave) than the Rapier. Again, I'm not sure the perception fits the reality.
If we're adding in Feats, the rogue can take Dual Wielder and get two rapiers instead of two shortswords and close the AC gap, or Crossbow Expert and use a hand crossbow, allowing them to transition seamlessly between melee and ranged.
I dont know. I use feats and MCing, and I see a lot of Strength builds. Literally every single Cleric, Paladin, Barbarian and most Fighters (those that arent built specifically as archers) use Strength.
And I allow both feats and MCing and I see a lot more Dex builds than Strength. Every single rogue, monk, ranger, most fighters and paladins (those that aren't built specifically as great weapon masters), every bladelock, every bladesinger wizard, and even some clerics and barbarians use Dexterity.
The only 'Dex to melee' guys I've seen in literally dozens of campaigns over 5 years have been every single Monk, and a Swashbuckler/ Battlemaster with TWF and Rogues.
Every Ranger barring 1 I have seen has been ranged, and the 1 ranger that was melee was a Tortle TWF Strength guy.
It's very strange to me that you draw a line between "Dex to melee guys" and ranged guys. Any Dex-based character can do both with no penalty whatsoever.