We've created a guide to choosing toolholders that you can see at a glance the advantages & disadvantages of different holder technologies.
Toolholder Performance Guide –*How to Choose a Toolholder
What i know is that the hydraulic fluid in hydraulic chucks make a vibration dampening effect and collet for the collet chuck does the same effect also. One of the most important features is gripping force since the axial forces are much higher than radial forces in high speed machining. And gripping force of the collet chucks are better than the hydraulics. I am not pretty sure about rigidity. Hydraulics are cheaper and there is no need of spare parts. Collet chucks' inner structure are symmetric hence their balance is better. Runout is almost same for both.
The advantages of hydros is the rigidity and gripping force approaches what you can achieve with shrink-fit. Cost of hydros is more than collet chucks. disadvantages is hydraulic bladder can be damaged and/or leak. also can only use 1 size tool shank for tool unless use sleeves. Collet chucks are good when maintained well and easy to change to different size shanks w/different collets. good balance and runout should be achieveable with either tool. rigidity & gripping force of collet chucks may be reduced as collets age and/or pocket is damaged. Keep 'em clean & don't over-tighten the nut is good maintenance for collet chucks. collet chucks are not known for vibration dampening. hydro's are.
Hope it helps,