Assume two bows, first bow is 2.2 attack speed, second is a 3.1 attack speed. Both weapons are 78 base DPS, 32 DPS arrows are used, 2002 RAP, hit-capped, on mobs that cannot block.
Since crits and armor would both scale the same (i.e. an increase in 20% damage or a decrease in 30% damage to both) we will assume 0% crit chance on the hunter and 0 armor on the target.
Assume spec is BM, so attacks get a 38% attack speed increase from base.
RAP will give white shots an extra 143 DPS, and steady shots 400 damage on top of weapon damage. Overall white damage should equal to 253 before factoring in speed. Steady shot will have a cast time of 1.09, and as long as GCD is over before auto-shot starts will not clip the next shot.
First bow will do an average of 557 damage on white hits, and 572 damage on steady shot. Attack speed of 1.59 (perfect timing would get no clipping of auto-shots from steady shot). Every 1.59 seconds, an average of 1129 damage would be done, or 710 DPS.
Second bow will do an average of 784 damage per hit, 642 damage on steady shot. Attack speed is 2.25. Every 2.25 seconds, 1426 damage would be done, or 633 DPS.
Okay, maybe I was wrong, and you should seek out the fastest bow that you can get a shot rotation into successfully (since obviously 2.2 would be near impossible due to lag, maybe a 2.5 would be ideal then). If there was a slight difference (of around 1-5% DPS I would chalk it up to rounding error, but with a difference of 10.8% or 12.2% (depending which way you’re going) I guess faster is significantly better.