I really doubt we'll see AMD do big/little on the desktop. Sure, they may have done research and patents, but every company does just in case, or to deny it to their competitors. AMD still have so much potential in their chiplets. They are already working on making them on smaller processes (which TSMC are able to do, unlike Intel), improve Infinity Fabric (which doesn't have the limitations of Intel's ring bus), install V-cache (which Intel gave up on in the form of 3D cache), keep adding chiplets to increase core (which Intel don't have), and continue to make IPC improvements.
Intel have to go big/little because they have none of the potential of chiplets. All they have is big monolithic cores with very limited room for advancement. Intel can't even get off the 10+infinity process node, no matter how dense they say they make it. Sure, Intel can pump a lot more power to get higher clocks, shave the IHS and chip to try and deal with the heat that produces, but the gas tank is empty on that approach. The cupboard is bare. So Intel stuck some small cores on the side to try and say they have efficiency, and sold it as something new. Intel marketing again leads the way for their engineering.
Intel went with big/little because they had very little else. AMD don't have to do that as they already solved those problems with their chiplet approach, and have much more potential reward in continuing to build on that technology.
Maybe we shouldn't be be predicting that AMD will follow Intel (who in turn copied Samsung/ARM/Qualcomm et al from their mobile phone SOCs), we should be predicting that Intel will have to follow AMD in chiplets, Infinity Fabric, and an actual 7/6/5 nm process node.