A densely-packed fin arrangement can provide very effective cooling, but only with high static pressure from the fans (which usually translates to high RPM and lots of noise). This is why you'll often see this in server heatsinks: saving space is important, and no one cares how much noise the fans make because they are in an isolated room somewhere.
Having a wider fin spacing means theoretical maximum cooling is less, but you can get decent results with low airflow. This is why you usually see wide fin spacing on products designed for quiet, passive/semi-passive cooling, like the Thermalright Macho and the Arctic Accelero S1 Plus.
Nvidia seems to have calculated that wider fin spacing would provide enough cooling for their ~250W cards while allowing for lower airflow that keeps noise levels down. For whatever reason, AMD went with a more tightly-packed fin arrangement, which means the fan has to spin at higher speeds to attain the static pressure needed to blow the hot air out.
The Nvidia blower looks to be about the same diameter, but is taller (as are the corresponding heatsink fins). This is probably hurting AMD's reference design a lot. Nvidia can get the same airflow at lower RPM.
I'm not sure Nvidia is gaining anything in terms of performance by using a metal blower instead of plastic (though it unquestionably looks better). Virtually all case and CPU fans, even premium ones, are made out of plastic, and this works fine. The same goes for the shroud: switching to metal/plexiglass is an aesthetic design win, but probably doesn't affect performance.
Could AMD fix this cheaply? Who knows. The shroud and blower impeller are probably injection molded, and creating new molds is not cheap at all.
As for copying Nvidia's design, I'm not sure they can do that. Nvidia almost certainly doesn't have a patent on the functional aspects of the blower (there's nothing new or innovative about that) but they may well have a design patent on it, given the amount of time and effort they put into development. Honestly, AMD would probably be better off just making a deal with one of its AIB partners to use their cooler in the reference design. Any of the third-party coolers (with the possible exception of XFX) are better than what AMD is cranking out.