Bit of both, actually. Even if you gave a beginner the best elo deck he could hope for that doesn't mean he can use it. And likewise, it doesn't matter how good you are as a player, you just can't win with a deck made out of 8 times 4/4 3* No ability against a seriously built deck.
The player. Seen lots of decks that everyone plays but only a few players can bring it up to 1400+. Also seen a couple of mediocre decks make it to the top 100, and a great bunch of powerhouses falling behind in the 1200s.
Decks can change overnight but definitely not the players (unless they have an alter-ego) ;)
A very good ELO player I know once said that playing UR is like driving in the F1 circuit. You are the driver, and your deck is your car. Sure, the best players win all the time. But you're never going to beat even the worst player if you're driving a Prius on the track.
Player. I and a few other people I know have been able to reach decent ELO ratings with decks that were handicapped in ELO (under 25 stars.) Another example; a new player in my guild has hit 1350+, I think this is his second week of ELO and he does not have the market unlocked.
The deck definitely matters, but a deck doesn't have to have the most expensive or the most overpowered cards to be effective. A good deck just means you have good synergy in there, you're capable of playing an offensive or a defensive game as needed, and and no one clan or setup is an "auto-loss" for you.
A good UR player choose and plays the good cards.
A good UR card doesn't choose and plays the good player.
+1 vote to 'the player'.
It's both. There has to be good synergy between a competent player and a competitive deck to succeed in any format. But a good player with a mediocre deck will usually beat a bad player with a great deck.
Also, it only takes 8 cards to play. More cards does not equal a better chance at winning, it just opens up more options for experimentation and adaptation.