Thank you all for your replies!
I am now 99% decided and might pull the trigger tomorrow.
My choice is neither.
If everything goes well, I am going to get a Sony RX1.
Both the Fuji and the Oly are great cameras without a doubt, but they are also systems...
And if I know myself enough, if I get either one of them, I am going to end up wantig more lenses, some primes, a good zoom and before I know it, I am going to need a dedicated bag to carry it all, going to be switching lenses instead of enjoying my trips and walks and end up spending a ton of money on a system that is going to end up sitting on the shelf most of the time in the long run...
So, in the name of simplicity, I am going to get the RX1, with it's superb combo of the FF sensor and Zeiss 35mm lens.
Keep it simple with an almost pockatble camera with stellar IQ that doesn't get in the way.
I have been living for the past one and a half year with just my iPhone as my picture taking device, so the single focal lenght will not probably be limiting and the IQ will be second to none.
Hope I don't end up regreting it.
Cheers!