Ranger
At level 5 a ranger just using a shortsword and scimitar, nick mastery and vex mastery (no dual wielder feat) will do 2d6+4 damage per attack with 2 out of 3 of the attacks being vex for a real chance to hit of 70.75% assuming a base 60% chance to hit.
DPR = 23.3
Adding in Dual Wielder (on turns where you don't need to cast or move hunters mark). Real chance to hit becomes 72.74%.
DPR = 32
Weighted average DPR assuming both happen 50% of the time
DPR = 27.7
Collosus Slayer Ranger = +4.5 DPR due to 4 attacks at high accuracy
Ranger Weighted DPR = 32.2
Fighter
Does 1d6+4 with dual wielder every attack for 30 damage total @ 60% base accuracy. Real Chance to hit = 72.74%.
DPR = 21.8
However, fighter has a number of short rest and subclass abilities that can improve DPR.
Action Surge = 15*72.74% = 10.9 Damage per short rest (will be slightly higher due to real chance to hit increasing slightly due to more vex attacks)
Superiority Dice +4.5 Damage *4 version = 18 Damage per short rest
Superiority Dice Riposte = (7.5+4.5)*.7274 = 8.7*4 = 34.8 Damage per Short Rest.
Damage per short rest 28.9 - 45.7.
Rounds per SR | SR - 28.9 Dmg | Total DPR | SR - 45.7 Dmg | Total DPR |
3 | 9.6 | 31.4 | 15.2 | 37.0 |
4 | 7.2 | 29.0 | 11.4 | 33.2 |
5 | 5.8 | 27.6 | 9.1 | 30.9 |
6 | 4.8 | 26.6 | 7.6 | 29.4 |
7 | 4.1 | 25.9 | 6.5 | 28.3 |
8 | 3.6 | 25.4 | 5.7 | 27.5 |
9 | 3.2 | 25.0 | 5.1 | 26.9 |
10 | 2.9 | 24.7 | 4.6 | 26.4 |
11 | 2.6 | 24.4 | 4.2 | 26.0 |
12 | 2.4 | 24.2 | 3.8 | 25.6 |
13 | 2.2 | 24.0 | 3.5 | 25.3 |
14 | 2.1 | 23.9 | 3.3 | 25.1 |
I'd assume 8 Rounds per short rest is average. Ranger can do a decent amount of damage more than the fighter when dual wielding. Fighter can really front load it though (that matters).
With 9 potential casts of hunters mark ranger likely can keep it up a whole adventuring day. Ranger also does better ranged damage. Sometimes something like spike growth might be more impactful, giving the Ranger an even better lead.
At Level 11 i'd anticipate the fighter mostly catches up.