Not 720, no, but it's not per-eye in either of the headsets. It's a 1080p screen, but each eye is seeing 960x1080 because it's a single screen split in half. That's really short-selling it, though, because the way the image is rendered and the way the optics in the headset are focusing those pixels makes a huge difference.
Full disclosure: I work at PlayStation, so feel free to take my opinions from here with any necessary skepticism, but in my mind (and I own a Vive, a Rift and PS VR) PS VR's optics and the OLED make for a better picture overall - especially if you have a PS4 Pro and the supersampling that it offers. Also, just to nitpick, it's Oculus (just a single C), and it's the same setup, but with a pentile layout (essentially the pixels are arranged in a row to deliver the image vs. PS VR's cramming the pixels into a single space. It makes for an overall better image when blown up by the lenses that distort the image to cram as many pixels into your central view as possible.