DH finds noise from our range hood to be extremely annoying, so I am trying to find a solution. Putting the motor outside or up the line is not an option.

The reported sones of a given hood surely do not tell the entire story.

Would it be significantly quieter to put the venting into a cabinet, or under the cabinet? -- instead of a wall mounted hood?

If wall mounted, does the style of the hood matter?

e.g. a pyramid vs. something like the Modern Aire PS1010?