Tiamat's +double is roughly +5-6%, according to a commenter with a sample size of ~277. Double Tiamat got his DA rate to ~20%.
When it comes to choosing from Reiki/Jack Frost/Tiamat as your main:
Reiki's 5% advantage in +water means a higher floor for your offense
Tiamat's +double is for the gamblers/people who really want to up their soul's combo rate cause she's holding back your full bursts :P
Jack Frost is for those leaning defensive against fire (I tend to be in this camp)/have specific defense plans (like if your future 100% damage cut plans rely on eidolon passives)
And then Illuyanka enters the picture not too far into the future. +50% water if you have water eidolons in all your sub slots.