What's annoying with both air cleaners and vent hoods, is that it seems some sellers have figured out that they want them to make noise, so people hear they are working. It's possible to make both much more quiet than they typically are.

One of the first upgrades I made to my house was buying a nice (interior) vent hood. The exterior ones need to be at least a few feet away from the stove, and my stove is right up against the wall it vents out of. I still was able to find an interior one that has 1/2 the noise and twice the airflow of the standard builder grade vent hood.

One annoyance is that almost none of the vent hood stick out far enough, ideally you want the vent hood to stick out a few inches (at least) past the front of the cook top, but almost none of them do that (likely due to head bumping issues, understandable) so a lot of effluent still escapes.