I'm sorry, but, I'm just not seeing it.
Sure, a fighter archer may be a better archer than a paladin archer, no problem. But a ranger archer is going to put that fighter to shame. The fighter just can't possibly keep up before 11th level. Not when I've got a guaranteed d8 bonus damage every round (or nearly every round) from colossus slayer, and then hunter's mark. So, I'm pretty much always doing 3d8 bonus damage every single round as an archer ranger. You can't possibly do as much damage. And, before you bring up feats, I've got advantage on my attacks in the first round of combat as a ranger, so, giving me Sharpshooter makes me even better.
By 6th level, the only advantage you have as a fighter is an ASI. Whoopee, you're +1 to hit and damage better than me. At most, six extra attacks per day. Again, compared to my up to 3d8 bonus damage every single round, you can't come even close to competing.
And if it takes you 11 levels just to catch up, that's poor game design.
Let's look at how close the fighter and ranger actually are at ranged combat...
The first look is without feats. The 2nd look will be with feats.
Level 1 - The fighter is ahead
Level 2 - Ranger is ahead (hunters mark is just that good at these levels
Level 3 - This is going to be a great starting point since the classes get pretty much the same features from here until level 6.
A lot depends on the number of combats you are looking at. Your ranger will have 2-3 uses of hunters mark per day. My standard comparison is 6 combats that last 4 rounds each with 2 short rests between. (The number of combats and short rests may be slightly high for some peoples experiences and I'm happy to consider alternatives but for now that's what I'm using).
I'll assume hunters mark lasts 12 combat turns in this scenario. Collosus slayer has a decent chance of not working on your first attack in combat so I am not considering it on the first turn of any combats. So it can be used 18 turns and approximately 2/3 of those attacks will hit. That's 12 uses of it.
So 1d8 times 12 uses = 4.5*12 = 54 damage caused by colossus slayer
Hunters mark will be used on 12 turns and will land 2/3 of the time for a total of 8 turns it lands. That's about 28 additional damage from hunters mark.
The additional damage for a ranger under these assumptions is 82 damage per day at Level 3.
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The fighter will make 3 additional attacks per day from action surge using a longbow for 1d8+3 damage. 7.5 average damage. If he lands 2/3 of the attacks that's 15 damage from action surge per day.
Precision attack can be used 12 times per day. Using 5 dice on the nearest misses for precision attack will mean you turn 4 misses into hits. That's 30 damage. You still have 7 precision attack dice at this level. =7*4.5 = 31.5 damage.
Altogether the fighters abilities give him 76.5 damage per day under the above assumptions. That's a difference of 5.5 damage over 24 rounds of combat. That's a tiny amount of damage difference. The fighter gets the additional benefit of being able to attack whatever target he desires at anytime and can do so from his max range (unlike the 60 range requirement for hunters mark).
Even at level 5 which would be the rangers next best level I wouldn't be so sure the fighter is that far behind him.
That said under a 3 combat per day assumption and 1 short rest per day assumption the level 3 ranger will likely wreck the fighter in damage