Retina display is bullshit in my opinion.
For example you mentioned it has a 800:1 contrast ratio.
My Samsung Captivate has a Super AMOLED screen with a 50,000:1 contrast ratio and produces much superior colors from my standpoint. iPhone 4 beats it in whites I believe.
I also heard that Retina display requires a back light, AMOLED does not.
Vita display probably also requires one, but if this thread is about wanting it to have a superior screen to what it has now, you would need to be asking for an AMOLED.
LCD beats AMOLED in colour fidelity (ie, AMOLED colours are super-saturated beyond reality), anti-aliasing due to the sub-pixels, and power consumption when displaying bright images, which is where I think you got "beats it in whites."
AMOLED beats LCD in viewing angle, contrast ratio, and power consumption when displaying dark images.
In practical tests, phones with LCD displays enjoy longer battery life than phones with AMOLED, which IMO is the most important attribute in a mobile display, given that both technologies look pretty damn good.
To answer the OP, the PSV is 960 x 540 (AKA qHD resolution) because that's conveniently one quarter the resolution of 1080p. That means scaling an image up and down from qHD to 1080p is really simple.
Convenience is also the reason why the iPhone 4 has a 960 x 640 display. They wanted a higher resolution without creating scaling problems for old images, so they used a display with four times the resolution of the previous iPhone screen. The DPI is utterly bonkers on a screen that small, and there's really no reason why the PSV should have a comparable resolution unless you're afraid your rez-wang won't measure up.