I think we're still some way away from producing ARM-based machines that are "twice as powerful" as comparable Intel/AMD x86 machines, but they are certainly getting closer:
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No one is saying "twice as powerful". I certainly wasn't. But the A12X and A12Z both outperform all eighth gen Intel Macs that are i7 or less. They likely outperform the 10th Gen Y series chips in the 2020 MacBook Air and I'm sure they give the 10th Gen U series chips in the 2020 Intel 4-port 13" MacBook Pro a run for its money if not totally outperforming those as well. What we'll get in an A14 based Mac specific SoC will only be better. Twice as powerful is unlikely at first. But it's likely that the second gen Mac specific SoCs will be at least twice as fast as contemporary Intel processors at native workflows. Though, Apple will, at that point, return to the Apples and Oranges of comparison between its Macs and the PCs produced by the rest of the PC industry that was commonplace during the PowerPC era.
The above is for cloud servers, so is not necessarily very relevant for most consumers, but we can draw the following conclusions:
1) An Apple Silicon SoC will probably be able to match or slightly exceed Intel/AMD CPUs in the same market segment, whilst using significantly less power.
They won't "slightly" exceed. The first wave of Apple Silicon Mac SoCs will clearly exceed the processors employed by the predecessor machines. You're not going to see a first generation Apple Silicon 13" MacBook Pro handily outperform an Intel 16" MacBook Pro, but you will see it handily outperform the last Intel 13" MacBook Pro.
2) Apple will probably balance performance vs battery life in ASi laptops - we may see something that is "about the same speed as Intel Tiger Lake" but with 15-20 hour battery life.
Again, Apple Silicon destined for the MacBook Air and 13" MacBook Pro will handily outperform Intel's chips. Tiger Lake isn't THAT MUCH faster than Ice Lake to change that as far as those Macs are concerned. Where Apple may have work they need to do is in competing with the H series CPUs. But the Apple Silicon 16" MacBook Pro has AT LEAST eight months more in the oven if current rumors are to be believed.
3) Desktops SoCs will probably try to increase the number of CPU cores and custom SoC features to beat the current high-core-count Intel & AMD CPUs.
Can't argue there. That sounds both correct and sensible.