I've been told by others, and have come to agree with, that expecting a single short rest but a total of 12 rounds of combat a day (3~4 combats with 3~4 rounds each) is a good benchmark to discuss this kind of thing.
So, the Fighter will have 10 superior dice uses per day, but between action surge and the fact you can use one die per attack, you can concentrate your maneuevers over a short time. Especially if you burn four of your five per short rest on the same turn you action surge. In 2024, though, power-attack aspect is gone, though overall damage is actually higher over time thanks to Masteries. Speaking of, with Tactical Master and Tactical Shift, the Fighter is actually better at using bows to control the battlefield while maintaining equal damage through Push and repositioning themselves.
Meanwhile, the Ranger has less nova ability, but more sustained damage and tricks. Hunter's Mark is the best 1st level spell for raw damage, and Entangling Strike is a great trick-arrow ability. Lightning Arrow can turn misses into AoEs. Conjure Barrage and Conjure Volley are AoEs full of arrows. Swift Quiver, Elemental Weapon and Fire Arrows are dps boosts over larger time frames. These are the archer based spells - I'm not going to count Spike Growth and Summon Beasts towards being an "archer" as they might contribute to fights, but they're more related to the trap-setting and animal-empathy aspects of Ranger. Ranger can use Longstrider for better positioning, but then we're not using any of the archer-magics, so kind of a wsh.
So, who's the better Archer? I honestly think that Fighter is probably better at being a raw "archer" - most of the best Ranger tricks to be great in combat involve skills and magics that aren't directly related to archery, while Fighter is better at accuracy, trick shots, and pure speed. This probably shouldn't be a surprise, since "master of weapons" is kind of Fighter's gig.
Meanwhile, I'd say that Ranger is probably better at being a bow hunter. Having magical hunting dogs via Summoned Beast, setting traps via Spiked Growth, etc. Definitely great hunter skills, but I wouldn't call them archer skills.
I liked the mechanics behind Samurai. I'm not sure if we could realistically translate it to 5e24 without it being underpowered, since advantage is so much more common now, though I think it might be worth considering how to update the subclass to 2024. Its was a fun subclass.