Do PS4 & Xbox One render at lower res if the screen is lower than preset res?

If I play a game on a HD (720p) or HD-ready (768p) display, will I get a bit better performance than on a FHD panel or are the games rendered at whatever the developer sets and then just stretched out or shrank based on the connected display?

Submitted by zaxrider | #Specialdealer Special Offer Online Shopping Store 2016