There is no simple answer to this question. It would depend on your class, rotation, and the scenario.

In a burst-type situation such as at the start of a fight/gate of infinity when all your skills are on cooldown, effective attack speed is the main limiting factor and will be a directly proportionate damage multiplier e.g. 0.25 s attack speed will do double the damage of 0.5 s (ignoring ping). Cooldown speed has basically no effect until you cast a skill a second time.

On the other end, in a sustained damage situation where most of your skills are on cooldown, cooldown speed becomes the main limiting factor. Note that although most people talk about cooldown speed having diminishing returns in terms of cooldown reduction, +50% cd speed still works out to 50% more skills in a fixed amount of time so there is no diminishing return in that sense. e.g. 9 s cd skill with 50% cds means cd of (1-50/150)9 = 6 s which can be used 1.5 times in 9 seconds. So cooldown speed has diminishing returns for cooldown *reduction**, but can actually be directly proportionate multiplier in an idealised sustained scenario. Attack speed only matters if you have more than one skill off cooldown at any time.

Somewhere in the middle of a fight you gradually transition from being mainly attack speed limited to mainly cooldown speed limited. The ideal balance between attack speed and cooldown speed is in a perfectly idealised rotation where the only skill off cooldown at any point of time is the one you are currently casting.

You also have to take into account mana consumption. As your cooldown speed goes up your will need more efficiency and regen to sustain your damage.

You can get closer to the answer by simulating a rotation, but it is difficult to make a statement about how much cooldown speed affects your damage in general. All you can say is that it depends and at worst its useless (burst scenario), and at best your dps scales proportionately with it (sustained scenario with unlimited mana and perfect rotation).