Just testing on dragonborn, 15% AS, 16 BaB, Rapid Shot, Rapid Reload, Quick Draw
# of bolts fired in 1 minute, divided by (1+doubleshot % (1/3 DS for repeating))
1 Heavy Crossbow No AP spent 90
1 Repeating Light Crossbow No AP spent 151
1 Repeating Light Crossbow No AP spent + haste boostx3 171
(untested Mechanical Reloader will probably improve RLXBow by 3.3% and heavy or GXbows by 10%, GXB should be about the same as heavy crossbow)
Inquisitor
3 AP spent Dual Crossbows 141
3 AP spent Dual Crossbows haste boost 163
Dual Crossbows + Inq. Path Auto attack 150
Dual Crossbows + Inq. Path Auto attack + haste boost x3 in LD 173
Dual Crossbows + Inq. Path No Holds Barredx3 in LD 197
The dual wield crossbows don't operating independently like TWF. It seems to be a change from the standard aim - attack - reload, to a new aim - double attack - reload - reload.
As a result, the offhand will add twice as many bolts per attack, but the time per cycle will be slower due to additional reload time.
Haste boost appears to affect aim - double attack, and as such provide 50% of its listed bonus in terms of auto attack rate of fire. So 30% haste boost is 15% actual rate of fire increase.
Inquisitor's Path 30% alacrity appears to only affect double attack, and as such provides 25% of its listed bonus or 7.5% increased auto attack rate of fire.
No Holds Barred appears to affect the reload - reload portion, and be overall twice as effective as haste boost, so is ~30% actual rate of fire increase.
In heroics, where you don't have much ranged power or double shot, ranged power or double-shot boost are both superior to haste boost, and close to equal to No Holds Barred.
Dual crossbows have inferior base rate of fire to repeaters levels 1-11, but repeaters have 1/3 doubleshot so don't scale as well 12-30.
Dual Crossbows have roughly equal base rate of fire to repeaters levels 12-30, but have the advantage of full doubleshot.
Untested, but Mechanical Reloader is probably 1/3 of 10% or 3.3% faster auto attack rate for repeaters due to aim - fire - reload and only affecting the fire portion.
Armor of Speed is bugged and does not affect repeating crossbows. I'm pretty sure haste/blinding speed does work on everything.