Why do server mainboards use different capacitors for their VRMs?
Except from the advantages/disadvantages of each capacitor type (you can find these online), there might be others, realted to manufacturing or project limitations like:
Manufacturing cost, space available, availability of capacitor types, weight etc.
For example in a factory location where they design high quality boards, Electrolytic capacitors might be more expensive than Ceramic (due to the location or shipping difficulties), so they will choose to use Ceramic ones to reduce the cost a little bit.
I dont have any specific idea why they would use each type of capacitor on each situation.