Peter Svidler
If there was a 'Fischer Random Chess' tournament at the global level, who would win it?

Magnus Carlsen.He sometimes played here some 960 chess games and he plays like if position were standard one.

The truth is that Nakamura excels in positions that are highly "messy", with the pieces on weird squares, and just strange positions in general. Carlsen is weaker in this area - he's good at simpler positions, where he can grind an advantage from almost nowhere.
960 provides Nakamura with his strong point, and that's probably why he's so good at it.
(This is also my strength as well, obviously to a lot lower extent than Nakamura though, which is why I enjoy live960 a lot)

I remember the commentators saying that sometimes the starting position favors white in 960, and they seemed to suggest a few times that Naka had an unfair advantage in one of the games.
Also 3 games isn't a big sample.
I'd still bet on Carlsen being the best, at least over Naka.
It would be Hikaru Nakamura without a doubt. He won the last Mainz championship in 2009 (no world championship has been held since) and is currently the highest live 960 player on Chess.com He is far better than any other 960 player in the world. Far better than even Magnus.
In the recent Blitz battle on chess.com, Hikaru defeated Carlsen in 960. He won easily in Chess960, just like he did in the quarterfinals and the semifinals.
It is hard to imagine that there is anyone who can beat Hikaru in 960 today. Hikaru simply loves chess 960. In the last world championship in 2009, Hikaru destroyed Aronian (the former 960 world champion) 3 1/2 - 1/2.