Cash games and multi-table tournaments require different styles of play.
But which one requires more skill to be good at?
Disclaimer: I am a cash game player, so you might consider my opinion to be biased.
Cash games tend to run deeper than tournaments. This in turn leads to more post flop play in cash games than in tournaments, as a general rule.
Post flop play in a deep cash game, even one that is only 100 BBs deep, can be very difficult. Given that we play against players with short stacks as well as deep stacks, we still need to have all the skill sets used in tournament play when playing cash, but cash players need to have additional skills that tournament players generally don't -- they need to be able to play 3 streets of post flop poker.
Therefore, as a general rule -- and I know that I'm opening myself up to a ton of criticism here -- it takes more skill to play cash than it does to play tournaments. There are simply more decisions that are easier to get wrong in cash than in tournaments.
I would argue that both games take a similar amount of skill in order to achieve expert-level play. However, to achieve average-level play, tournaments require less skill.
The reasoning behind this is, as John Dibling stated, cash games require more postflop play. That complication is forced into the game much more than any of the complications of high-level tournament play, and as such, average-level players must learn more to hold their own in cash games (while in tournaments, they can rely more on comparatively simple preflop decisions).
That said, to play tournaments at the expert level requires balancing a lot of variables that can be mostly (or completely) ignored by play at the average level. There are a huge array of subjects when you start looking at ChipEV vs $EV considerations and many many complications created by differing stack sizes (both for you and your opponents) and by the state of the tournament. Many of these complications have no equivalent in cash games (though expert-level cash play has its own set of complications). Which leads me to the conclusion that moving into the expert level puts the two back onto a fairly even footing.
Further, it's worth noting that tournaments can be more demanding from an endurance perspective, since you do not have the option to leave the table when you are no longer playing your A-game.
However I would say cash game is more complicated, that's not the point.
The point is, they need different skill sets;
Of course there are aspects of tournament play you can't find in cash games, but calling Sit and go tournaments "solved games" is not an accident... I think we will never say that deep cash games are "solved", because it's far more complicated than chess, that have bigger decision trees, and factors that can't even be computed (human factors).
A note that very deep stack tournaments are almost the same as cash games, due to a huge amount of postflop play. (maybe even more complicated)
So when you talk about Phil Ivey being far more superior player than anybody in the world is because he plays deep tournaments all the time, where his edge is much more greater than in "turbo" tournaments.
This one is easy. Amateurs win WSOP bracelets often. Amateurs don't sit in cash games with the Phils and take their money.
Not a direct answer but I would rather be in a tournament against a better player.
A pro can bully an amateur and if the fish wakes up with a hand the pro can just re-buy. In a tournament the pro has more risk.
In a cash game the amateur is more worried about bankroll.
Betting is more dynamic in a cash game as you can take more risk (you can reload).
GTO is not as effective cash in my mind. High stakes yes GTO plays strong cash but I don't think we have many high stakes cash players on this site.
Cash you can sit in and have a bunch of regs that know each other's play.
Against a home game I would way rather play cash. In a casino if you play low stakes to get fish the rake kills you.
I am more successful at cash games than tournament play. Cash games come so easy to me, where as tournament play I find my style isn't suited as well. My strategy in cash games is: