In both demos, the PS4 system and PS Vita were paired over a local Wi-Fi network in simpler terms: gameplay was being streamed over a wireless router from the PS4 to the PS Vita. Visually, both Need for Speed: Rivals and Battlefield 4 were displayed with surprisingly little compression. Though not quite as sharp as the gameplay on a nearby TV, the PS Vita's OLED display makes colors really pop. The rear touchpad was divided into a quadrant with L1, R1, L3, and R3 mapped to each corner. While it took some getting used to, the assignments were surprisingly effective and easy to reach.
The two titles drastically varied in terms of latency, however. On the one hand, Need for Speed: Rivals ran almost 1-to-1 with only the occasional stutter, whereas the lag was far more noticeable on Battlefield 4. Racing games, especially one so focused primarily on adversarial chases, require a fairly high level of responsiveness and there were one or two times when I noticed lag between a command and the on-screen action.
Shooters are even more dependent on low-latency precision, and Battlefield 4 definitely struggled with the natural delay between the PS4 and the PS Vita. Aim adjustments were identifiably slow and caused the aiming reticule to bounce around the screen. For the demo, I played a level of the singleplayer campaign, and even with the lag, it was still playable, but I can't imagine it would be as forgivable in a competitive multiplayer match.
Now, of course, there are a few very important things to note. For one, both demos took place over an event network, which in my experience, is pretty unstable due to congestion and interference from multiple simultaneous routers in close proximity. In a more realistic home environment and a stable Wi-Fi network, the experience could be drastically different.