I have mechanical 105 on my spare/zwift bike and Ultegra DI2 on my main bike. The Ultegra equipped bike is indeed quieter.
Noise is unavoidable as there will always be friction. There's more wax on the outer part of the chain and in the inner part when it's fresh out of the pot, explaining why, in my opinion, it is always quieter for the first few hours. Doesn't mean that it needs to be rewaxed as soon as it starts making more noise though.