Attack bonus or Damage?

[Moonglum]

Personally, I would take STR, if nothing else then because you're a fighter... You won't be using that longbow all of the time, and some of your feats will helped along with STR.

If you were a ranger, I would say to go with the highter DEX. Maybe you should think about that route...

 

[Ranger REG]

For an archer, go with Dexterity. In case the enemies close in on you, use melee weapons with Weapon Finesse to take advantage of an already high Dex score (recommendation: rapier).

While I agree that BAB will increase by level, assuming you survive long enough to reach the next level, the best way to dispatch your enemies is to increase your chance of successful hits. The more you hit your opponent, even for little damage, the faster you should be able to defeat your enemies.

 

[Victim]

Dex will help more as an archer.

Strength damage on bows is hard capped at +4 because mighty bows only go that high. And it's easy to increase strength. At low levels, you'll have a hard time affording a magic bow, and at higher levels you could increase strength via level increases or magic items.

 

[Mustrum_Ridcully]

I think there is no definite answer.
But if you want that your stats "fit" to your character`s description, you should take a high Dex.

But remember that sometimes you will be forced to fight in melee, and Strength helps a lot here in getting the enemy down.
Your Dex might boost your AC, but there will be enemies who will nearly always hit you, so it is better to get them down fast.

And later you can buy magic items to boost Dex or Strength - both is available (at least in a high magic setting ), or you can ask your spellcasters - clerics, wizards, bards all have spells to buff up stats. (If you have a Cleric, he can raise your strength, a bard might be able to do both, a wizard or sorcerer most typically relies on Dex in this case, because some spells needs ranged touch attacks and they want the AC Bonus - Strength has no use for a wizard or sorcerer, so they will never get spells for it, or at least very late...)