Fuji argues that adding stabilization will add bulk to the lens. But I have personally owned the Leica/Lumix LX5, and Sony RX100 series that have stablization in the lenses. Sure, these are smaller sensors, but I think it can be done. Fuji said IBIS could not be done in their X-Mount. Fuji said they could not make IBIS smaller than in the X-H1.
On the other hand, Sony a6000 is an absolute power house when it comes to IQ. Even though Sony's APSC line has limited lenses, you can always get the FF lens for the body, if you are planing to eventually upgrade to a7 series in the future. I'm not a big fan of a6000's ergonomics and the buttons are very fiddly.
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fujifilm x10 vs sony a6000