It seem to be somehow different, is it still FF-based? Or is there any possibility to use tails and then use Tor bundle same way as you use it in Windows?
And of course, is Tails's browser's security in same level as Tor Bundle?
No; it uses a modded version of Firefox, not straight TBB. https://tails.boum.org/forum/Tor_Browser_Bundle/ https://tails.boum.org/doc/about/features/index.en.html
Tails is based on Debian which uses Iceweasel which is just a rebrand of Firefox.