Judging from the promotional blurbs on waste disposers, noise is a really big issue in this market.  Frankly, I don't see the importance here; sure, some run more quietly than others, but you wouldn't want to start up any of them while your better half is asleep in the next room.  And when you do run it, it's only for a matter of seconds; it's not like it's going to be hindering conversation for the entire evening.

If noise is an important issue with you, there are several factors to consider.  The most obvious is sound insulation; the better disposers have a plastic shroud built around the upper half (the area of the grind chamber itself; the motor is actually pretty quiet), while the cheap units do not.  There are different degrees of such noise shielding, with In-Sink-Erator describing its top two models as having "double baffle" sound insulation.  Of course, you could buy a cheap unit and then wrap something around the upper half yourself.

The rubber flappy thing within the drain itself is also a consideration.  It is, in fact, one of the most important features to keeping the noise in the grind chamber from getting out into the room.  Obviously, if you want to minimize noise, you'll want to put the plug in the hole while grinding -- which means you might want to opt for a batch feed unit instead of the more common continuous feed unit.

With any rotating machine, minimizing sound transmission from its moving parts to the surrounding structures involves soft rubber mountings to isolate vibrations.  With a disposer, there are two attachments between the unit itself and the rest of the world: the structural attachment to the bottom of the sink, and the attachment to the drain pipe.  Ideally, both of these connections will be made using a flexible rubber isolator.  (The wiring could also transmit vibrations, but hopefully nobody will make the mistake of connecting it up using rigid conduit.  As long as flexible conduit or, better, a power cord is used, vibration transmission won't be a problem there.)

All In-Sink-Erator models use the same mounting scheme to the sink, and it includes rubber isolation.  The rubber flappy thing in the opening is, in fact, the rubber isolator; the outer section of the same part is the mounting grommet for the disposer.  It is slipped onto the lip of the disposer, and then the mounting ring compresses this rubber grommet so it grips the lip securely; there is no metal-to-metal contact between the disposer and the sink.

Unfortunately, the connection to the outlet pipe may not be as good.  Some disposers use a scheme here where a rubber grommet is fit around the end of the outlet pipe, and then the pipe and grommet are secured to the outlet of the disposer itself with a bolted-on flange that compresses the rubber grommet enough to secure a watertight seal.  This will provide good vibration isolation, since the pipe itself touches the grommet only, not the metal flange nor the disposer casing.  However, the Kenmore model 60563 I bought in 2001 has a threaded outlet on the disposer, and the pipe connects to it quite rigidly.  This may not be much of a concern with PVC piping since the plastic probably absorbs a good bit of the vibration, but if I were plumbing this thing up with metal pipe I'd be concerned.  Interestingly, an In-Sink-Erator model 444 observed in a store, while apparently largely identical to the Kenmore 60563, had the better rubber-isolated outlet pipe connection.

You might want to note that the rubber isolation and PVC piping means that the disposer is not electrically grounded to the sink or piping.

In the horsepower discussion, I pointed out that there are two different types of motors used in disposers: induction and commutator.  The induction motors run at 1725 rpm, while the commutator motors run much faster; GE claims 8000 rpm for theirs.  This makes a world of difference in the sound.  The 1725 rpm units make a sort of droning sound as they run, while the commutator units scream by comparison.  Even if the actual db levels are comparable, some homeowners may prefer one sound over the other.  To some, the induction motor's drone may seem a more relaxed sound while the commutator motor's higher pitch sounds more hyper and irritating.  On the other hand, some people might find the higher pitch of the commutator motor less intrusive, while the induction motor's drone seems almost earth-shaking, like it fills the house.  On top of this, there's the issue of starting and stopping; the commutator motor starts smoothly and winds up like a jet engine, while the induction motor starts with a sudden kick.  Overall, I expect most people will find the induction motor's sound preferable, especially with the high-end units where the unit was clearly designed with minimal noise as an objective.

It may not be obvious, but if you're concerned about noise you might want to look at the sink you're installing this disposer in.  Heavy porcelain cast iron sinks don't transmit much sound, so if you mount a reasonably quiet disposer to one you shouldn't get too much racket.  Thin stainless steel sinks, on the other hand, can take whatever vibration you feed into them and amplify it like a megaphone.  If you have a really cheap stainless steel sink, you know it's noisy; you hear the racket it makes whenever you drop a spoon in it.  If you have a better stainless steel sink, it's quiet -- because it comes with a sprayed-on coating of dampening material on the underside.  This coating not only makes the sheet metal nice and quiet, it also helps keep the water hot by providing some thermal insulation.  So, if you just looked at the bottom of your stainless steel sink and saw nothing but stainless steel, you know of one option for reducing noise: find some of that spray-on stuff and apply it.  I don't know if a dedicated product is available, but automotive undercoating might do.