Here's my mock-up:
Literally is just a stretched 360 controller with the Vita's controls slapped on top, but you get the idea. I'm not sure about the placement of the Start, Select and PS buttons. I'm not really keen on them.
In my head it's a tad bigger than your standard controller but not full on WiiU GamePad size. Sort of in-between. Touchscreen would be used for text, social stuff, OS menu stuff both in and out of game and developers could also utilise it for DS-like bottom screens if they wanted to. It's not a massive screen but it could work. Biometrics would just be on the sides and back of the controller where your palms/fingers are.
It is a bit 360-ish I admit. I may try to base it more off the DualShock's design later.