Is Fractal Design Define R4 still the king of cooling/noise ratio?
No one around here has made any statement of that kind. It'd be nice if we could just pick one case out and declare it king for clear, unambiguous reasons... but that's fantasy. There are too many system types, too many sizes, too many styles.
The reality is that most decent cases can run extremely quietly, and even poorly made cases can be made to do this (tho this might require some smart & skillful modding). The case itself doesn't make noise; it's your choice of components to go into the case that ultimately determines the noise of the system.
A good case, as I see it, should be....
. This means good joinery, reasonably thick metal panels (with added mass damping if they are too thin), more rather than fewer rivets/screws, more supporting braces rather than fewer, etc. Basic mechanics. Good quality cases from a decade ago are generally far better in this regard than most of today's cases, which are flimsier, more flexible, less well supported, more prone to vibration noise. Perhaps some remember the Chieftec series & all their copycats, or things like the Antec SLK3700: Heavy, thick steel cases full of rivets. But they were also less well vented. Quality server type cases are generally far better made than consumer cases. The HP Microserver case, for example, stands head & shoulders over most consumer mITX cases: Thick panels, great mechanical joinery, excellent fitting modular design, excellent quality bolts/screws with threads that don't strip after a few uses.
2) Good ventilation
. This means enough low-impedance vents for fans & airflow, and larger rather than smaller. Some might interpret this to be a thumbs up for all-mesh cases, but that doesn't always lead to good ventilation unless you're completely fanless. Cooling airflow from fans generally works best when directed, and shorter paths for the airflow in the case are best. So, for example, with a 140mm back exhaust fan in a big vertical case (say >50 liters), top vents and front vents (and no other openings), most of the inflow will be through the top. This means any components in the front won't get much airflow if that back fan is the only one. Close of the top vents and you'll get some cooling for the front components because the front vent becomes the main intake. Control the airflow path so it passes through/around hot components and you can run fans slower while still getting decent cooling.
Sound blocking/damping (by which I mean super thick panels & heavy elastoviscous mats glued to the panels) is not as important as it used to be because there are fewer truly noisy components, and better airflow = lower fan speed = lower noise. But baffles that minimize direct sound paths between the user and the noise source are still quite useful -- ie, the type of front baffle/fascia widely popularized by the P180 series.