Hi Petre

Among that three cameras, I would skip Panasonic and concentrate on fujifilm and olympus only.

Here are my thoughts since I own both Olympus & Fujifilm camera ( I own XE2 and OMD EM5.)

As far as my experience goes, Olympus tends to have more rich details on dark scene (shadow), and the color tone somehow Olympus nails it perfectly. My only complain on olympus is they don't perform well on bright scene (highlight)

While fujifilm tend to have a good balance for both shadow and highlight.

both Fuji and Olympus does produce a great lens quality.
I think they did cover up most of range within their lens.

Functionality, Performance Wise, ease of use, I think generally both are about the same.
I use Fuji XE2 (and I do tested out XT1 and XPro1) and Olympus OMD EM5.
depending the situation given, I somehow prefer my XE2 for general shooting. easier to recover an highlight or shadow in lightroom / photoshop.

on evening scheme, I would go with my Olympus..

Can't explain it, but the feeling just there. Olympus nail the scene and color tone perfectly. love it.

That is my two cents anyway. soo... uhm.....
take my words with grain of salt..
Im not a professional photographer anyway.. haha

I would advise you to test both camera and see which one you like.

Good Luck mate