Mateusz, I appreciate your answer very much. To be honest you confirmed my presumption.
I have enabled active breaking on ESCs. I have softmounted the flight controller, put the gyro filtering to 0.000 and the quadcopter flies perfectly. During the time I fell in love to fly with Librepilot. I am flying with some Betaflight FC, too. BF behaves like a robot compared to Librepilot (no offence, just a comparison).
I am not religious about any particular flight-firmware, I would use whatever works for me. Having said, I tried and tuned Betafight (BF) on 3 builds ranging from 280mm to 80mm, so not judging without knowing anything. These quads are my father's so I kept BF on them for simplicity (that works ok for him) and on my own builds I use LibrePilot (LP) that works for me. Perhaps, I am not really good pilot to differentiate two tuned quads, but I am sure it would help LP developers a lot, if one could define "behaves like robot". It's like reporting an issue on JIRA, first you need to be able to define the problem, provide test case that can reproduce the issue, then developers can pick it up and work on it.
They can never fix issue, if they can't reproduce it themselves . Maybe there is already a solution, but just different option has to be enabled and since these are different software it's hard to say what to change to get desired behaviour.
Each software has pros and cons, some features LP has, which BF has implemented differently, or not implemented at all, and the same goes of course other way around, to name a few 3 banks only LP, more advanced Autotune LP, dynamic Notch-filtering BF, anti-gravity-gain (BF) but this one is IMO some hack to solve symptoms rather than proper solution, it works but is not elegant and maybe there is more elegant solution already (I guess enabling thrust PID scaling would do the same thing). Since you are flying already both firmwares, and I assume you have both builds tuned to best of your abilities, it would be of really huge value, if you could point what's expected. For instance, when I do this manoeuvre banking or something, with this settings quad behaves like this with LP, but with BF it behaves like that, what to do, to make it behave like this (even with different hardware, maybe it will give idea what's different). As long as it is something better than "feels good" I am sure devs will follow it up
Unfortunately, some blogs I read compared different quads, without saying what's wrong and showing one quad well tuned PIDs, other compared in that particular video I watched was LP quad using different hardware and totally way off PIDs shaking like crazy
There goes conclusion, it really had something like fair comparison in title but in description said it's stock PIDs as well...
Sorry for long reply!