Active noise cancellation generally works best for consistent background noise. Sound that changes rapidly, like human voices, will be difficult for the cancellation hardware to react to, and headphones that provide sound isolation may be more help. See https://www.quora.com/Is-there-a-noise-cancelling-headphone-....
I have headphones which provide sound isolation, as well as noise cancellation: Sennheiser PXC-450. In a room with a noisy server cabinet, I can actually hear people talking better with my headphones and NC on than without. The headphones cancel much of the fan noise, to a greater dB level than the isolation from the headphones attenuates the voices.
