Sorry for my absence xD I've forgotten about my thread.
I've given another chance for 4.3, clean install with root. Unfortunately problem still exist. I know that isn't a high end device but I've got second, even slower device that works better. Yes, I've got some ram hungry apps but only a few (facebook, messeger, swiftkey that's all). I've got only 30 very basic apps installed and I've disabled some unused by me sony apps.
Task managers.... no it's bad idea. I've got two other android devices and they work without any task killers, I never clean recent apps too.
But the most strange thing is that sometimes it can work fine for whole week and sometimes it slows down after two days.
Thanks for your replays.