I've never thought of choosing a case for being "quiet," and as JeffMD noted, it's not a major factor.
It is a major factor for the vent and fan options it offers, and a calculated "optimization" strategy either for air-cooling or water-cooling may include blocking off unused vent holes. This depends on whether you're a stickler for directed airflow in that strategy. Alternatively, you could build a case out of perf-steel (and we've seen a few sold on the market), provide no pressurization, and make it "breezy."
About 20 years ago, I picked up a stethoscope in an auto-parts store which was marketed for an auto-mechanic's use. I keep it in my toolbox of computer resources. You quickly discover, probing different surfaces, the level of motor noise being generated from particular points (fans in particular, and "unisolated" HDDs. Many times, people who complain about "noisy HDDs" of a particular manufacture may be correct about a drive model, but they wouldn't have noticed it if they'd taken installation pains for installing them in a case.
A "good" case will have drive cages with rubber isolators, separating the HDDs from case-metal. For the fans, the use of metal screws to secure the fans will transmit motor noise of the fan to case metal. You would hear that noise easily with a stethoscope simply by probing the fan hub on the non-moveable frame side of a fan. Then, touching the case metal around the fan mounts, you can see how it's transmitted to the case, and possibly echo or propagate.
So you can buy rubber fan isolators of various sizes:
http://www.sidewindercomputers.com/setof4fanrid.html
If you can't use them for a particular fan or mounting point, then exchange the metal screws for nylon machine-screws and nuts. But hard plastic or nylon still transmits sound. Go to the auto-parts store, and look for a roll of self-adhesive rubber hose bandage. Take a small rectangle of the hose bandage -- just enough to wrap around the nylon screw without appreciably increasing its thickness -- and neatly wrap the screw threads. You can also purchase those little "rubber-donuts" used to fill electronic chassis holes passing wires through which eliminate "wire-chaffing." You can even cut them down the center groove, and use either the entire donut or its half on either end of the screw as an isolating washer.
Another thing you can do involves purchasing an $8 box of this:
http://www.coolerguys.com/840556014003.html
You can cut the material with scissors for any number of applications. Small 1.5" right-triangles will fit the corners of your fans which don't have a rubber corner (the better ones do these days). Use an office single-hole punch to make the hole for a mounting screw or strap matching the fan mounting holes.
This proves out with the stethoscope if you probe "before and after."
Nobody but an OCD DYI'er will want to eagerly embrace these things with time and attention, but they don't take a lot of time.
Since fan noise consists of "white-noise" from air-turbulence and motor noise, your efforts will go a long way in muffling the latter.
YOu can even use the Spire material to construct a circular rubber "nose" to stick on the fixed side of the fan hub. If you build a duct for a fan, you can build it with several layers of Spire to further reduce transmitted noise.