What eletrical element of a kettle determines its speed to boil?

The wattage of the element determines its' time to boil together with the amount of water in the appliance.

There is a dial, and there is a copper rod that sticks out of the dial. The dial is manufactured to control the 'hotness' of the copper rod. The copper rod sticks into the kettle like a plug and heats up a copper circle underneath the kettle. 

Fun fact...did you know the bubbles in the boiling water in your tea kettle are the same size as the bubbles in the largest generating plant boiler or steam locomotive?

The power ( wattage) , but they are all around 2kW so for a given volume of water , they are pretty close .

The higher the watts the more speed it has. Usually they cost the most too.

Surface area of the element tends to be the main thing. Electrical properties will be higher with higher surface area.

Its power consumption (in watts)  

combined with its thermal transfer characteristics.