I realise both of the mentioned classes are tank types but they are still different classes with different skillsets and cannot always be directly compared.
The main rotation skills of the Champion are 6-7s, Templar 6-8s.
Other situational and utility skills are longer and vary greatly but I don't believe they are twice as long as Templar skills, at least not skills that can be compared directly, but correct me if I am wrong and tell me the skills you are comparing.
Attack speed doesn't reduce cooldowns, it increases the speed of your auto-attacks and reduces the time of your skill animations. You cannot reduce the time of cooldowns, or the 1s global cooldown that some groups of skills have.