Mercedes Balance Analysis

Assumption: Speed Mastery is learned before level 10
Both jobs have the same critical hit rate, therefore, it will not be included until 4th job where Sharp Eyes exists.
Final Attack on mob skills will be added as a second +%/s It is mostly negligible on mob skills, and is a bigger bonus towards Mercedes due to their faster attack rate.

First Job

 Spoiler

Speed Dualshot
Delay: 720ms -> 690ms
Damage: 115%x2
Max Monsters Hit: 3
Single: 333.3%/s
Mob: 1000%/s


Double Shot
Delay: 810ms
Damage: 155% x2
Single: 382.7%/s

Arrow Blow
Delay: 810ms
Damage: 220%
Max Monsters Hit: 3
Mob: 814.8%/s

Conclusion: First job, almost all characters can OHKO what they're training on. Therefore, since Mercedes gets a movement skill and attacks faster, it has a significant advantage as well has having more DPS to begin with, although it may be possible in certain cases for its lower damage to not meet the OHKO threshold, anyone who actually cares about DPS would be able to.

Second Job

 Spoiler

Cross Piercing
Delay: 810ms -> 660ms
Damage: 83% x4 * 1.15
Average Critical: 1.21x
Max Monsters Hit: 6
Single: 700%/s + 126.5%/s
Mob: 4199.8%/s + 126.5%/s
3997.4%/s - Builds tend to recommend leaving Cross Piercing at 16 due to insufficient amount of skill points to max core skills.

Speed Dualshot
Delay: 720ms -> 600ms
Damage: 115% x2 * 1.15
Average Critical: 1.21x
Max Monsters Hit: 3
Single: 533.4%/s + 139.2%/s
Mob: 1600.2%/s + 139.2%/s

Charge Drive + Final Shot
Delay: 600ms + 480ms + 900ms -> 480ms + 390ms + 720ms = (1590ms)
Damage: (130% + 210% + (90% + 30%) x4) * 1.15
Average Critical: 1.21x
Max Monsters Hit: 8
Mob: 5741.0%/s + 52.5%/s

Arrow Bomb & Iron Arrow
Delay: 810ms -> 720ms
Damage: 310%
Average Critical: 1.1575x
Max Monsters Hit: 6
Single: 498.4%/s + 96.5%/s
Mob: 2990.2%/s + 96.5%/s


Golden Eagle & Silver Hawk
Delay: 3030ms
Damage: 250%
Single: 82.5%/s

Conclusion: Cross Piercing is stronger than either Arrow Bomb or Iron Arrow. Most builds recommend Cross Piercing be capped at level 16 to be able to max other skills, but this difference does not make up for the overall strength it has, combined with Soul Infusion. The only advantage regular archers have is a larger range. Golden Eagle and Silver Hawk suck.

Third Job

 Spoiler

Strike Dualshot
Delay: 630ms -> 540ms
Damage: 126% x4 * 1.15
Average Critical: 1.21x
Max Monsters Hit: 4
Single: 1298.7%/s + 154.6%/s
Mob: 5194.9%/s + 154.6%/s

Leap Tornado
Delay: 750ms -> 240ms + 630ms + ~150ms = 1020ms
>>Jumping Time + Leap Tornado + Falling Time = ~1020ms
Damage: 135% x4 * 1.15
Average Critical: 1.21x
Max Monsters Hit: 8
Mob: 5893.4%/s + 81.9%/s

Double Leap Tornado
Delay: 750ms -> 240ms + 630ms + 630ms = 1050ms
>>Jumping Time + 2x Leap Tornado = ~1020ms
Damage: 135% x4 * 1.15
Average Critical: 1.21x
Max Monsters Hit: 8
Mob: 8015.%/s + 111.32%/s

Gust Drive
Delay: 930ms -> 240ms + 780ms
>>Constant 1890ms Spam Delay
Damage: 195% x3 * 1.15
Average Critical: 1.21x
Max Monsters Hit: 6
Mob: 2584.2%/s + 44.2%/s

Charge Drive + High Kick Demolition
Delay: 600ms + 480ms + 870ms -> 480ms + 390ms + 720ms = (1590ms)
Damage: (169% + 273% + (120% + 30%) x6) * 1.15
Average Critical: 1.21x
Max Monsters Hit: 8
Mob: 9395.7%/s + 73.5%/s

Gust Drive + Charge Drive + High Kick Demolition
Delay: 240ms + 750ms + 480ms + 390ms + 720ms = 2580ms
Damage: (195% x3 + 169% + 273% + (120% + 30%) x6) * 1.15
Max Monsters Hit: 6
Mob: 5153.6%/s + 77.7%/s

Charge Drive + Double Leap Tornado
Delay: 480ms + 390ms + 240ms + 630ms + 630ms
Damage: (169% + 273% + (135% + 30%) x8) * 1.15
Average Critical: 1.21x
Max Monsters Hit: 8
Mob: 6839.8%/s + 133.9%/s

Strafe
Delay: 810ms -> 720ms
Damage: 180% x4
Average Critical: 1.1575x
Single: 1157.5%/s + 96.5%/s

Inferno
Delay: 810ms -> 720ms
Damage: 460% + 100%/s DoT
Average Critical: 1.1575x
Max Monsters Hit: 6
Mob: 4437.1%/s + 600%/s DoT + 96.5%/s

Inferno
Delay: 810ms -> 720ms
Damage: 480%
Average Critical: 1.1575x
Max Monsters Hit: 6
Mob: 4630%/s + 96.5%/s

Arrow Rain/Eruption
Delay: 960ms -> 780ms
Damage: 148 x3
Average Critical: 1.1575x
Max Monsters Hit: 10
Mob: 6588.8%/s

Phoenix
Delay: 3030ms
Damage: 360%
Max Monsters Hit: 3
Single: 118.8%/s
Mob: 356.4%/s

Frostprey
Delay: 3030ms
Damage: 330%
Max Monsters Hit: 3
Single: 112.2%/s
Mob: 336.6%/s

Frost Knight
Delay: 1530ms
Damage: 550%
Single: 359.5%/s

Flame Knight
Delay: 1530ms
Damage: 550% + 110%/s DoT
Single: 359.5%/s + 110%/s DoT

Shadow Knight
Delay: 1530ms
Damage: 625%
Single: 408.5%/s

Conclusion: Unicorn Spike is not a very significant improvement to DPS. In most training scenarios, it will be a OHKO attack. In a bossing scenario, the damage improvement to Strike Dualshot is within the 5% overall damage margin. Gust Drive itself only appears to have utility in movement and mob gathering. It does bad DPS as a standalone skill, with a very long delay for spamming. When combined with Charge Drive, it lowers the overall DPS as well as being unable to hit the 7th and 8th monsters. With Booster on, Leap Tornado can be performed twice in a single jump, giving it a significantly large DPS output, beating Arrow Rain/Eruption with similar (though smaller) Range. Strike Dualshot is better than Strafe in every concievable way except its 350% range vs 440%. It otherwise is a stronger mob skill than Inferno and Blizzard as well as being better in single target. High Kick Demolition's "DPS" isn't particularly relevant since it's likely to OHKO in regular training situations and would not be used at bosses, which cannot be tossed. Elemental Knights attack at 1530ms and absolutely dominate Phoenix and Frostprey in DPS.

Fourth Job
Single Target:

 Spoiler

Ring of Ishtar + Legendary Spear
Ring of Ishtar attacks at 120ms per shot. Legendary Spear has a 15s cooldown. When switching from Ring of Ishtar to Legendary Spear, a 300ms delay exists to stop attacking. Another 300ms delay exists to restart Ring of Ishtar. Legendary Spear has a delay of 690ms after Booster.
The following effects are active:
Advanced Final Attack
Dual Bowgun Expertise
Ancient Spirit
Soul Infusion
Legendary Spear
Under the assumption that Ancient Spirit + Soul Infusion = 1.3 * 1.15 = 1.495x damage modifier;
Base Damage: 2882.7%/s
With self buffs and Critical: 5408.1%/s
vs 40% PDR Monster: 4369.7%/s
With SE vs 40% PDR Monster: 5083.5%/s
vs 75% PDR Monster: 3461.2%/s
With SE vs 75% PDR Monster: 4026.6%/s

Hurricane
Hurricane attacks at a constant 120ms per shot.
The following effects are active:
Advanced Final Attack
Bow Expert
Spirit Link: Phoenix
Sharp Eyes
Marksmanship
Under the assumption that Legendary Spear's defense reduction is a multiplier with Marksmanship (PDR * 0.8 * 0.75)
Base Damage: 3058.3%/s
With self buffs and Critical: 4831.6%/s
vs 40% PDR Monster: 3382.1%/s
with LS vs 40% PDR Monster: 3672.0%/s
vs 75% PDR Monster: 2113.8%/s
With LS vs 75% PDR Monster: 2657.4%/s

Ultimate Strafe + Snipe
Ultimate Strafe attacks at 720ms at Normal (6) + Booster and 600ms with Speed Infusion/Advanced Yellow Aura
The following effects are active:
Snipe
Marksman's Boost
Spirit Link: Frostprey
Sharp Eyes
Marksmanship
Under the assumption that Legendary Spear's defense reduction is a multiplier with Marksmanship (PDR * 0.8 * 0.75)
@ 720ms
Base Damage: 2428.6%/s
With self buffs and Critical: 4002.0%/s
vs 40% PDR Monster: 3008.4%/s
With LS vs 40% PDR Monster: 3207.1%/s
vs 75% PDR Monster: 2139.0%/s
With LS vs 75% PDR Monster: 2511.6%/s
@600ms
Base Damage: 2800.0%/s
With self buffs and Critical: 4577.8%/s
vs 40% PDR Monster: 3397.6%/s
With LS vs 40% PDR Monster: 3633.7%/s
vs 75% PDR Monster: 2365.0%/s
With LS vs 75% PDR Monster: 2807.6%/s

Mercedes are vastly superior in single target damage. Marksmen and Bow Masters are very close to each other, but Mercedes are about 1.5x ahead.

Mob Damage:

 Spoiler

Rolling Moonsault + Legendary Spear + Lightning Edge
vs 40% PDR Monster: 1919.8%/s
With SE: 2233.4%/s
>>8 Monsters: 17867.2%/s
vs 75% PDR Monster: 1520.6%/s
With SE: 1769.0%/s
>>8 Monsters: 14152.0%/s
With 16 Unicorn Spike, approximately 1.06x stronger with and without SE, and 1.09x stronger if Unicorn Spike were maxed.

Strike Dualshot + Legendary Spear
vs 4 40% PDR Monster: 7357.7%/s
With SE: 8559.6%/s
vs 4 75% PDR Monster: 5827.9%/s
With SE: 6779.9%/s

Pierce
vs 6 40% PDR Monster: 13726.5%/s
With LS: 14903.0%/s
vs 6 75% PDR Monster: 8579.1%/s
With LS: 10785.1%/s
@ Fastest (2)
vs 6 40% PDR Monster: 14448.9%/s
With LS: 15687.4%/s
vs 6 75% PDR Monster: 9030.6%/s
With LS: 11352.7%/s

Ultimate Inferno
vs 6 40% PDR Monster: 5529.3%/s
With LS: 6003.3%/s
vs 6 75% PDR Monster: 3455.8%/s
With LS: 4344.5%/s
+840% DoT

Bow Masters suck at mob damage. Mercedes' Rolling Moonsault is calculated considering a scenario where tossing is not possible, like party play maps. This does not consider the fact that Charge Drive and Lightning Edge move the Mercedes into monsters, so while this does have a really high damage output, it isn't likely to be feasible in most scenarios. When hitting 6 monsters each, Pierce and Mercedes appear about even, but Mercedes can reach up to 8, while Pierce requires CO to hit 7. Strike Dualshot does about as much damage to four monsters as Rolling Moonsault + Lightning Edge, and more than Pierce on four monsters. These do not consider that Legendary Spear can hit up to 12 monsters, or more than 4 monsters when paired with Strike Dualshot.
Unicorn Spike has the possibility to increase DPS by a small margin when combined with skills that are not Ring of Ishtar.

Overall:
Mercedes has a much more utility, and generally better earlier job. Their mobility and mob control provide better training. Rolling Moonsault may have difficulty in utility due to the required use of Charge Drive, causing damage taken in heavier bossing scenarios, as well as the bonus damage from Charge Drive's toss not dealing extra damage. Single Target DPS potential appears to significantly favour Mercedes in end-game scenarios though, but Mercedes' Legendary Spear's defense reduction appears to be a very useful skill for a party regardless.