Quote Originally Posted by Atoli View Post
Is it better to use a bow with lower DPS (like Ifrit's bow) for which I can reach the stat caps or the Lieutenant's Bow but being unable to reach the stat caps?

(Artemis Bow is not an option yet^^°)
No.

Stat caps are just the point where raising the stat becomes less efficient than raising Attack Power. It won't overtake a stronger bow because those stats would just make the stronger bow do more damage than the weaker bow anyway.