I guess this is the long awaited post, but here's a breakdown of Bows+Arrows in general, relative to when you have access to it and the monster distribution... Note that this info may be helpful to gage how powerful the weapon balance, particularly for characters that aren't Rosa (Aim ensures maximum hit rate which means maximum damage effectiveness, but it doesn't magically improve her attack power).
Irow Arrows - First Buyable @ Kaipo
Bow (Short Bow) - First Buyable @ Kaipo
It has virtually no impact other than being the first arrow set Rosa can use. Bows and Arrows in general are useless for Rydia+Edward due to low hit rate are better options. Rydia's Rod or IceRod has a better chance of doing mediocre to decent damage (particularly with the IceRod) vs the enemies. Edward's Harps have a very high hit rate, despite not being back row compatible (except in FF2US).
Holy/White Arrows - First Acquired @ Damacyan/Mt. Hobs, Buyable @ Mysidia, Holy elemental, 4x attack power vs Undead and Spirits
CrossBow - First Acquired @ Damacyan, Buyable @ Mysidia
One of the few times you get it, I actually recommend that combo particularly on Mt. Ordeals, less so on Mt. Hobs, only because you obtain a limited supply of Holy Arrows. Reliablity can be hit or miss, but if you gain a number of levels with the twins, they will eventually gain enough Strength to increase the attack multiplier to be semi-reliable. This combo can easily murder most units, with the exception of the Lilith (and Slap is a nasty attack at this point in the game). These arrows become useless @ the Underground Waterway in Baron.
Fire/Ice/Lightning Arrows - First Buyable @ Toroia, Lightning Arrows give 4x attack power vs Mechs
Greatbow - First Buyable @ Toroia, +3 Str
These elemental arrows are not that great when you first get them.. since the Holy Arrows are actually better for Cecil in the Magnetic Cave. There are a few monsters that are not weak against Holy elemental, making it the viable arrow of choice. The Greatbow starts pouring on some Strength bonuses that may help in getting the additional attack multiplier to make it even more useful than before.
Darkness Arrows - First Buyable @ Dwarf Castle, inflicts Darkness Status
These arrows are nifty if you want the Darkness status to wreak some havoc on certain enemies. Darkness status halves magic evasion (useless for enemies) and evasion (same reason as before), but also halves hit rate which can effectively reduces an enemies's attack by half and halves spell hit rate, which may allow some magic attacks fizzle out more frequently. Unfortunately these arrows are generally overshadowed by the Ice Arrows you would primarily use in this part of the underground, but those don't have enough power to kill the Black Lizards.. unless you overlevel or give Rosa some decent Strength boosting equipment instead of Spirit/Will Power boosting equipment.
Medusa Arrows - Pretty much obtainable by stealing or praying for those drops (first monster you find that will drop these are the Black Lizards), inflicts Stone status
These are the weakest arrows of the bunch in terms of power, but their primary task is to insta-kill monsters via Stone status. Status inflicted effects are primarily based on the target's level vs the attacker's level. The higher the level the attacker is, the more likely the status is inflicted. It's handy to know this when you are hoping for that Stone status to be inflicted... you might be in for a surprise.
Archer/Killer Bow - Obtainable @ Tower of Bab-il Underground, Buyable @ Eblan Caves, +5 Str
This is a nice improvement, and can better guarentee a chance at an increased attack multiplier. Although, that's not too much of an improvement...
Poison Arrows - Acquired by Monsters related to the Hydra and Naga, first seen @ the Underground Waterway, Buyable @ Eblan Caves, inflicts Poison
If you get them in drops early in the game, they are technically more valuable to you then than at the time you can buy them. Poison status is a useless effect when the rate of poison damage is directly corellated with the monster's HP. In other words, you won't benefit from the Poison damage. These arrows by themselves don't really do much when you can buy them. One of the few rare notes is that the Holy arrows are the most effective around Cave Eblana.. with Fire arrows and Ice arrows holding up the rear in terms of overal effectiveness.
Mute Arrows - First Acquired @ Castle of Eblan, Buyable @ Tomra, Inflicts Silence Status, 4x attack power vs Mages
It's kinda annoying that the time you buy them, you won't be able to use them vs the Mad Ogre (I digress). Anyways, these arrows are nifty, but unfortunately you obtain a bow that is an insta-Mage destroyer, minus the Silence status..
Elven Bow - First Acquired @ Sylph's Cave, 4x attack power vs Mages, casts Shell as an item, +5 Wisdom/Intelligence
This is an insta-Mage destroyer weapon. This is probably the first bow that is useful for any character than can take advantage of it, given that it's strangely abnormally high hit rate will allow 99% hit rate @ level 96, which is the maximum. This weapon IMO is the best in FF4, since anyone can use it and Mages are very visable late game and can be taken advantage of. Unfortunately this weapon won't get them killed unless paired with reasonably powerful arrows...
Charm/Fairy Arrows - First Acquired as a semi-rare item drop from Lamia and Queen Lamias, Buyable @ Land of Summoned Monsters, Inflicts Charm Status, 4x attack power vs Giants
These arrows seem useful, but I think they are not as useful as they could be. There are very few Giants (and their formations) late game that you would expose these arrows to, unlike certain areas of the game. Adding Charm status is a nifty touch, but technically too little, too late for their impact. Even the Lightning Arrows, as weak as they are have more impact overall in the Giant of Bab-il than these arrows in general.
Samurai/Yoichi Arrows - First Acquired @ Land of Summoned Monsters, Rarely Dropped by Marlboros @ Sylph's Cave, Buyable @ Blacksmith's
These are the most useless second version of the "generic arrows". Unless you are playing FF4ET, these arrows are useless. They need significantly more power so I'd give a damn.
Samurai/Yoichi Bow - Acquired @ Land of Summoned Monsters, +10 Str
Although this may appear to be the "strongest" bow, I don't believe it's as impactful as people think it is. Hit Rate for those who don't have Aim and Strength bonuses are more beneficial to Rosa.. not Cecil or Rydia (Rydia gets uber Strength bonuses post level 70). Still, the Elven Bow is better, but that's my opinion.
Artemis Arrows - First Acquired By Kary/Moon Goddess drops (though stealing is a better option), 4x attack power vs Dragons
Given that the distribution of dragons are insane in the Lunar Subterraine, you would be foolish to avoid this. Paired with the Elven Bow, you shouldn't be fearing very much. The only issue though is that the enemies that are not dragons won't really be torched... but I guess that's better than nothing.
Artemis Bow - Rare Drop by Kary/Moon Goddess, 4x attack power vs Dragons, but that's only in FF4ET, +10 Str, Agi, Vit, -10 Wis, Will
This is a completely overrated bow if you aren't playing FF4ET. If you pair this Bow with the Heroine/Minerva Robe, you will have a dumb, but strong female archer. The Heroine/Minerva Robe in FF4ET does not have the stat penalty so it becomes relatively favorable to use in that version of the game. I don't see the specialness of this bow otherwise...
Note: I've already written some threads on what I think the bow+arrows should be in powerwise and the optimal Rosa configuration (maybe I'll dig up the links later if anyone cares)... the reality is that there are many parts of the game where the arrows and the bows have little or no impact. Increasing the hit rate early on (maybe lowering the attack power, but that's a balance issue) will help their progression and people liking it better for those not named Rosa.