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)
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.
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.