One knock I have seen against the Olympus is an EVF flaw. Evidently a green spot will appear in the EVF if used outdoors as the problem is evidently caused by exposure to the sun. From what I can gather this is something that happens with ordinary use and not something extreme. Here is something more about it on DPReview:
http/www.dpreview.com/forums/post/53896750
If lens selection is important then you will want to go with the Sony as there are more lenses available for it than there is for the Fujifilm. The sensor size on both cameras are nearly identical (23.5mm x 15.6mm for the Sony and 23.6mm x 15.6mm for the Fujifilm). However the Sony has a 24 MP CMOS sensor as opposed to the 16 MP CMOS sensor in the Fujifilm camera.
This - http
/www.digicamdb.com/compare/fujifilm_x-t10-vs-sony_alpha-a6000/ - explains some of the more technical details and differences between much better than I can.
Another review that might be worth reading can be found here -
http/cameradecision.com/compare/Sony-Alpha-a6000-vs-Fujifilm-X-T10 - It gives a side-by-side comparison and some technical details as well.
If I were choosing based solely based on what I have read I would go with the Sony A6000. Maybe someone with much more knowledge than I about any of these cameras will chime in and be able to help.