Having used tools like coremark and geekbench to try and compare x86 to arm with obviously incorrect results I can tell you it is next to impossible. Simple job accomplishment time is the best gauge. Try rendering something large on your old 1ghz x86 then try it on your phone getting a rendered image of the same checksum. After a week stop the phone.
It is certainly true that many computer tasks use next to no x86 resources and are prime for the better os's mobiles now have. I'd certainly love a lean Open source OS on my phone with a repository for the daily updates Android lacks.
ARM uses Reduced instruction set cpus which is less work per mhz. ARM chips are impressive at what they do especially per joule of heat but think about it. If a 1.6 ghz atom gets red hot and a 1ghz arm is tiny and gets a little warm, do you really believe they are anywhere equivalent. Phones also have slow data write and buses. The Super IO chip alone in desktops is often 20% of the size of my phone and needs a large heat sink.