How can you say a 1080p is "far superior" to a 4k when the sole defining feature of the 4k is the number of pixels, which by definition is a multiple of the lesser. Seriously it's not like those techno features aren't available for 4k sets as well. It's like comparing a Retina screen to a non-retina. Sources however...
Just saying it's possible for 1080p screens to be FAR superior to 4k screens, that said given everything is on LCD panels it is likely that many shortcomings on motion resolution/contrast ratio and uniformity will be challenges for both 1080p and 4k TV's to overcome.
So if all those other characteristics are equal, then the 4k will be better. That said, if you have a TV like a Pioneer Kuro, the last gen of Panasonic plasmas, or one of the best made, top end LEDs from the last two years - any of these 1080p TV's will look objectively better than a 4k tv that stumbles on motion resolution, colour accuracy, uniformity or contrast ratio. The only 4k TV's that can touch say, a Panasonic ZT are OLED or some VERY expensive top of the range LCDs that only just came out and are far out of the price range of the typical home buyer (ie $3500+)
The Motion Pictures Experts Group still prizes contrast ratio as the #1 factor that drives image quality - something HDR addresses (max brightness is higher for instance) and so this, rather than 4k, probably has a better chance of giving us objectively better image quality that's really noticed. The other issue with 4k is that on screens 65" or less the improved resolution is barely perceptible to the human eye (big difference for projectors tho and massive screens 70"+). Similar issue affected 1080p when it came out - if you had a 40" tv or less the extra pixels really did nothing for you.