DK2 still looks like holding your phone up to your face. It's a pentile display so you don't quite get a screen-door grid effect but you do get a sort of diagonal dot matrix that ruins the whole experience. Also the "higher-resolution" isn't really the issue, because the screen-door effect is still more annoying than the visible pixels.
We're a long way from having a 1080p type HDTV experience. DK1 was akin to 320x240 DOS gaming days. DK2 is like the early days of higher-resolution gaming where we all went "oooh" and "ahh over having enough CPU horsepower for 512x384 graphics modes in Quake.
For a crisp and clean picture, we're probably going to need 4K panels at 5" sizes (without pentile) or 8K panels with pentile. The reason that 1080p won't suffice is because there are magnifying lenses that mean you focus on a very small part of the screen, rather than an HDTV where you sit back and enjoy the whole picture from a distance. My guess is that the retail Oculus will launch with a 1440p OLED display from Samsung and the screen-door effect will be a bit better - Good enough that it's not a huge distraction, but still clearly visible to all but the medically-certified blind.
As for "what screen size?" well, it depends how close you sit to your screen
Seriously, there are dials on the DK2 that let you tune how close the panel is to your eyes, but I'd say it's like sitting 10 feet from a 120"-160" screen.
DK2 is somewhere between the first two images
here, and the suspected 1440p panel slated for the 2015 retail Rift is the middle image.
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