There is one critical area where manyshot beats rapid shot...on the surprise round.
As an archer, you might want to try a lot of sniping. Technically, you get one standard action, then people roll initiative.
With many shot and rapid shot, you can get a fully volley of arrows on that surprise round, and the penalties won't be as bad considering the opponent will be flatfooted.
Then if you win initiative switch to rapid shot. This will allow you to do a lot more damage in those first rounds of combat.
As an archer, you might want to try a lot of sniping. Technically, you get one standard action, then people roll initiative.
With many shot and rapid shot, you can get a fully volley of arrows on that surprise round, and the penalties won't be as bad considering the opponent will be flatfooted.
Then if you win initiative switch to rapid shot. This will allow you to do a lot more damage in those first rounds of combat.