We all know that both Precise Shot and Rapid Shot are important to ranged builds, but if you had to only take one which one is mechanically more vital to a build?
[Note that the following values are not exact because they don't incorporate natural 1s, 20s, or scenarios in which you cannot hit or are guaranteed to hit with a certain BAB. The following values should be very close to their true values however and this nuance likely does not change the conclusion (which is a little fuzzy anyway).]
Let's assume that the enemy is in melee and you only have a single attack normally (+5 BAB or less). Then, the precise shot is going to be 30% more likely to hit than each of the rapidshots. The average damage equals out when your precise shot to-hit is 60% (60% = 30% + 30%) and is in rapidshot's favor when it is higher.
Next, let's assume that the enemy is in melee and you normally have two attacks. Again, each precise shot is 30% more likely to hit. The average damage equals out when your precise shot primary attack to-hit is 90% (90% + 65% = 60% + 60% + 35%) and is in rapidshot's favor when it is higher.
For three attacks, they even out when your precise shot primary attack to-hit is 110% (100% + 85% + 60% = 80% + 80% + 55% + 30%). So, by the time your BAB is +11, precise shot is always better when the opponent is in melee.
So, when opponents are in melee, it looks like rapid shot is really only better for those early levels before you get multiple attacks. It seems unlikely that your primary attack to-hit with precise shot is going to ever be 90%, however since opponents aren't always going to be in melee, precise shot and rapid shot might close to equal in the BAB +6 to BAB +10 levels.
Rapid Shot, by a country mile.
Additional attacks are always a DPS booster more than even modest attack and damage bonuses, and the Precise Shot attack bonus is situational to the point that it may not come up in a given combat, while an additional attack nearly always comes up unless you're always moving.
There are obviously exceptions for a given build (like some scouty build that requires you to be taking a move action every round) but in the general case, rapid shot is to be taken immediately and precise shot eventaully, and the latter more for prereq purposes than its actual utility. Precise Shot is archer feat #4 or 5 at best (Deadly Aim comes way before it as well).
If you do x damage and have a y% chance to hit, then your expected DPS is x * y. Omitting fenceposts and crits, for low levels let's use a base "I need to roll a 10 to hit" (you have about a +5 attack bonus and are seeing AC 15 threats) and "I do 5 points of damage on average". So your base DPS for those example numbers is 2.5.
If a target is not in melee combat, then precise shot doesn't help you. Your expected DPS with rapid shot is 2x(y-.1), which is 4 for our example numbers.
If the target is in melee combat, then precise shot retains your DPS at 2.5. Rapid shot becomes 2x(y-.3), which is only 2 for our example numbers.
However, even if your targets are in melee 70% of the time (an extremely questionable assumption in my experience), your net DPS with rapid shot is 2.6 ( 4 * .3 + 2 * .7), still higher than our 2.5 original number.
And of course, as you can see from the equation, the more you don't suck - your chance to hit and damage go up - the more the equation comes out in your favor. If your base chance to hit is 60% or more then rapid shot is always better even when your opponent is in melee (I'll let you solve the system of equations yourself to prove that).
Precise shot is only better when a) a target is in melee and b) it's pretty hard for you to hit that target in general.
But a good archer (in a party with good tactics) is usually choosing their targets so that's not the case... Your 70% value raises warning flags for me. Most combats aren't solos, and given 5' steps, your fellow party members should be ganging up on high AC people while disengaging from other targets as much as possible. If "the majority" of the opponents are "in melee 70% of the time" you should be shooting at the minority that aren't. Precise shot can, at best, get you up to your normal expected damage; don't play that game, use things like Rapid Shot to double it!
This can't be mathematically proven because every campaign and combat tactical situation is different, but in, uh, 17 years of 3e play every single character I've seen who invests in ranged feats goes rapid shot as early as possible. Pathfinder's Deadly Aim is the only thing that has snuck in as a contender, but even there you're comparing +2 damage at -1 to hit vs 2x damage at -2 to hit, usually not the right thing to do.