Archer General's setup

Imo, Mori is better than Tokugawa. His active skill can deal damage equal to carpet bombings and it is only on 4 turns cooldown. Tokugawa active skill is very situational and more often than not is not worth to postpone attack, because 2 normal attacks are even better than a single one with 150% damage. Special unit of Mori is a way better than Tokugawa's and it is significant easier to farm Mori's fragments. I think that Chosokabe is better than Tokugawa for the same reason too.

Update: Mori hits harder when Tokugawa doesn't have his buff, but still Tokugawa is unmatched when using his active.

The choice imo depends mostly on whether you need more crowd control or more general killers.

But why no one count Master of archery skill? +15% dmg always looks better than Mori. And Mori has only 4 bow icons (whatewer it means), so he's weaker. I'm mostly using Tokugawa with mounted archer in campaigns and his skill is useful too, mostly when he's not in range he can easily prepare his blow. Mori's skill only deals 60-90 troops dmg and debuff dmg, so when enemies are fat this means almost nothing.

I'm still using Tokugawa as my main archer on Mounted Archers, possibly because I'm stubborn, but I like him.  I also have Chosokabe though, and he's probably just as good (or better according to some) and will be much easier to upgrade in the long run, usually I'm deploying both of them.  At this point in the game I'd be skeptical of spending Blue Flames on anyone who doesn't have a Legendary Story though, because sweeping those is just too good.

If our assumption is correct, generals deal 10% more damage when leading their special units.
Besides, Mori's skill is usually great against a group of enemies. Cumulative damage is usually greater than a damage against a single opponent. Besides, it is only one part of his skill, the other one is to debuff opponents. And, I think, at lvl 6 Mori gets a life-stealing ability (very useful on units with multiple attacks, such as Horse Archers)

Between the two, I have found Ieyasu the superior. I always thought that Mori Motonari's carpet dealt too little damage to make it a viable spam cleaner. Plus Motonari's damage with archer even on crit is pretty dismal. Admittedly I have both on only two stars so that might be an unfair comparison.

I think bow icons represent bonus attack not damage. And like in previous ET games it is probably 5-6 points of attack.

If Tokugawa uses Horse Archers instead of his own unit his damage output is 10% worse than that of Mori on horseback. That negates his damage bonus of AM. I think their capabilities as pure Archers are more or less equal. BUT as a team player Mori is far superior to Tokugawa, imo. Not only that. If we analyze this situation in long-term perspective we have to keep two important factors in mind.

1. Mori is a way easier to upgrade (provided we have access to his HL) In the long run it is a huge advantage. We can farm up to 4 fragments per day. The only way to upgrade Tokugawa is to send him on missions with fragments as reward. But that means we won't upgrade other generals who don't have HL as well. For example, Hideyoshi.

2. At lvl 6 both of them have new skills. Tokugawa has 20% additional damage bonus against one opponent next to the target. It is nice to have but isn't very spectacular.
Mori, on the other hand, gets a lifestealing ability. Taking into consideration the fact that Horse Archers will have almost 100% probability to attack again eventually, that means that Mori is almost unkillable even without necessity using healing items.

I had Tokugawa before I restarted the game and, as you pointed out, without Horse Archers his offensive potential decreases quite significantly. Yet, Horse Archers are not his special unit.