edit: changed rapier to longsword, and corrected some numbers.
Archers are superior to melee for pure damage, if twinked. Although Hardhead's melee fighter was NOT twinked, it holds true even when he is (I've twinked him up a bit below).
However, Hardhead's original complaint is baseless - manyshot does not improve the archer in any tangible way, other than coolness. Average damage actually drops when it is used.
Also... archers are NOT more deadly without the very archer-friendly magic items. In a low-magic item world, the archer's advantage disappears like mist. I have included this in the analysis.
Below is my best attempt at analysis. I may have made errors, in which case my opinions may be flawed - please pick it apart to be sure!
Hardhead said:
Two 16th level characters.
Mr Archer: Bard 1/Fighter 15 (to get the requested BAB +15)
Mr Melee: Bard 1/Fighter 15 (to get the requested BAB +15)
Mr Archer now has 50 attacks at this bonus. Mr Melee now has however many attacks he can make in a day. This may or may not matter.
Your feats and weapon selection are a bit off. The melee fighter should go for the best, just like the archer:
Mr Melee should use a Longsword + Short Sword. Using a greatsword is simply silly compared to this combo! This also brings him in line with Mr Archer's number of Greater Magic Weapon castings.
Feats (human, 15 feats):
Mr Archer: Weapon Focus (Longbow), Weapon Specialization (Longbow), Improved Critical, Manyshot, Point Blank Shot, Precise Shot, Rapid Shot.
Mr Melee: Weapon Focus x2 (Longsword + Short Sword), Weapon Specialization x2 (Longsword + Short Sword), Ambidexterity, Two-Weapon Fighting, Improved Two-Weapon Fighting, Improved Critical x2 (Longsword + Short Sword).
Mr. Melee's full-round attacks are +28/+23/+18 (+15 BAB, +7 STR, +5 Weapon Enhancement, +1 Weapon Focus).
BAB +15, STR +7, Magic +5, Weapon Focus +1, Two Weapon -2. Grand total of +26/+26/+21/+21/+16.
Damage: STR +7, Magic +5, Weapon Spec +2. Grand total of +14. The damage for these is (in order) d8/d6/d8/d6/d8 (each with the same bonus). On a successful hit, damage is: 18.5/17.5/18.5/17.5/18.5
Assuming a CR 17 mature adult red dragon, the AC (assuming +8 worth of buffs) will be 32. Chance to hit is 65/65/40/40/15%.
The longsword has a 20% chance of threatening a crit. The chances are 13/8/3%. The short sword has a 20% chance of threatening a crit. The chances are 13/8%.
Average damage over a round: 45.1
Mr. Archer's full-round attacks are +34/+34/+29/+24 (+15 BAB, +7 DEX, +5 Weapon Enhancement, +5 Arrow Enhancement, +1 Weapon Focus, +1 Point Blank Shot, +2 Bracers of Archery, -2 Rapid Shot)
BAB +15, DEX +7, Magic +5 (bow), Magic +5 (arrows), Weapon Focus +1, Close Shot +1, Rapid Shot -2, Bracers of Archery +2. Grand total of +34/+34/+29/+24.
Damage: STR +4, Magic +5 (bow), Magic +5 (arrows), Weapon Spec +2, Close Shot +1, Bracers +1. Grand total of +18. The damage for these is (in order) d8/d8/d8/d8. On a successful hit, damage is: 22.5/22.5/22.5/22.5.
Assuming a CR 17 mature adult red dragon, the AC (assuming +8 worth of buffs) will be 32. Chance to hit is 95/95/90/65%.
The bow has a 10% chance of threatening a crit. The chances are 9.5/9.5/9/6.5%.
Average damage over a round: 82.91
(as a side note, without allowing magic bows and magic arrows to stack, the average damage over a round drops to 65.59. Interesting how much that one rule impacts things! And here without that rule and without the bracers, it drops to 55.69.
Manyshot gives an 80/80/80/80% chance to hit, at 22.5 average dmg per hit, for a total average damage of 60.64. Manyshot does NOT make the archer more powerful, and at 16th level, it actually lowers average damage!
One additional comments
Every time Mr. Melee fells an opponent, he has to move into position to hit another, letting him only take one attack that round.
I have
never seen a fighter fail to take Cleave and Great Cleave, and I've rarely seen a situation where felling an opponent does not immediately result in an
extra attack for Mr Melee, as opposed to fewer attacks.