Jerry - you didn't mention which chemical (herbicide) was used. ???
Some herbicides may only brown-out the contacted portion of the plant. Others may be more capable of killing the plants' root systems - provided that the application timing, mix concentration, surfactant and treatment coverage are appropriate.
Basically, if you don't have a lot of cattails to manage, use your cutting-method. Otherwise, an appropriate chemical treatment is usually more labor-effective.
