I distinguish between a casual voice chat and an important meeting/presentation, casual I often take on the go and use whatever is the most convenient option (definitely not a proper headset... bone conductors more like it). At an important meeting I usually don't walk to another room.

And if you specifically mean the cheapest possible models, yes wired will have cable noise, but wireless will have horrible connection and battery issues, so let's assume we are talking about a good above-average model and in that case you can expect no cable noise.