Flash & Unity3D browser conflict

I'm not an expert on this, but I believe the Unity3D and Shockwave Flash browser plugins I have installed (in Google Chromium) decide to go fisticuff whenever I visit a page with a Unity3D browser game embedded there. Usually, Unity3D's left hook is enough to knock Flash out (Chrome asks me to terminate the frozen process "Shockwave Flash", which I accept) and finally get the Unity3D plugin to work. The very same thing happens in Mozilla Firefox as well.

Is it also possible that the website (www.kongregate.com) is using Flash on the background, and switching to a page which requires Unity3D causes conflict on the front-end (Sorry if I am using this term wrong) of the website?

Thanks in advance.

It’s a problem with flash plugin from chrome (they have their own) - same page in firefox works OK. I too have this problem with kongregate and have to open it in firefox.