Questions about the Sicilian Kan

First, why does the Kan score significantly higher than the Taimanov, despite many claiming that the Kan is more passive (which is negative?) than the Taimanov? Surely, if there is more counterplay for the Taimanov, that means that it would be higher scoring for Black than in the Kan.

Second, in the Kan, how should someone choose between developing the queen's knight to c6 or d7 (since it's supposed to be one of the reasons it is preferred by some over the Taimanov)?

"The Taimanov System ... was my main weapon against 1.e4 until 2008. ... [After a burst of popularity of my pet system,] I had to accept deep theoretical disputes in every game. ... I began my migration toward the Kan. ... The play is not forced and both sides have tons of options on every move. This greatly reduces the chances of being caught on a home preparation. The wide choice also means an ample ground for strategic mistakes. Even good grandmasters often mix up the move order and allow an easy equalisation. ... Keep in mind that the Taimanov is a self-sufficient system while in some Kan lines it is best to develop the knight on c6 switching over to the Taimanov. One such example is 1.e4 c5 2.Nf3 e6 3.d4 cxd4 4.Nxd4 a6 5.Be2!? ..." - GM Alexander Delchev in the 2014 book, The Most Flexible Sicilian

An important consideration is  how much like playing hedgehog positions, i.e white pawns on c4 and e4. These are more static and english like than most sicilian positions. 4...Nc6 by putting more pressure on the centre prevents most hedgehog positions. Only the old main 5Nb5 d6 6c4 Nf6 7Nb-c3 a6 8Na3 is respected version in Taimanov. In Kan have all sorts of different versions.

After playing Nc6, there is no reason black can't play a6 soon after. For example, in jengais first game 6...a6 is a sounder  line if white plays 7f4 b5 etc too. 

How the heck do you get into a Kan with a 2. ... a6 move order?

After 1. e4 c5 2. Nf3 a6 the move 3. d4 is known to be a mistake. White should play 3. c3 or 3. c4 instead... no?

Yes. It is widely agreed upon that 3. d4?! cxd4 4. Nxd4 Nf6 5. Nc3 e5! 6. Nb3 Bb4! is nice for Black.

Still confused.

1. e4 c5 2. Nf3 a6 3. d4 cxd4 4. Nxd4 Nf6 5. Nc3 e5! is practically winning for Black, AFAIK.

How exactly do your games transpose from an O'Kelly (2. ... a6) into a Kan?

People like Silman, for one...

But seriously, the position after 3. d4 cxd4 4. Nxd4 Nf6 5. Nc3 e5 6. Nb3 Bb4 cannot possibly be better than the position after 3. c4 e6 4. Nc3 Qc7 5. Be2 Nc6 6. O-O for White.

I think optimistic likes 4...Qc7 instead of 4...e6 in last diagram.

4... e6 IS the Paulsen.

And secondly, 5. Bd3 Nc6 simply cannot be easy equality on move 5. It would never be a main line then.

2...a6 3.d4 just gives Black an improved Najdorf. There's no reason for White to allow this... Anyway I never even got the difference between the Kan and Taimanov and I hear GM commentators mixing up the names all the time.

@jengaias: I would disagree. I feel that Black is doing well out of the opening in general right now, with all main lines looking as good for Black as ever, but opening theory itself was, is, and always will be in constant flux. In fact, I would say it's the Annoying d4 openings that are bugging Black right now. White always seems to get a little something just by having easier play. Black can also find it hard to get the counterplay that he has in all main lines.

In the words of Fischer, e4 is "best by test".

Commonly used advantage classifications:

"... stands slightly better"

"... has the upper hand"

"... has a decisive advantage"

The December 2016 issue of Chess lists the top twenty openings compiled from a list of 2895 October games where both players were rated over 2400 Elo. One can not take position on this list too seriously because it is greatly influenced by how the openings are grouped. For example, all the Retis are grouped together, while English is separated into 1 ... c5, 1 ... e5, etc. Nevertheless, for what it is worth, some of the list entries report: 133 King's Indians,108 Caro Kanns, 97 Nimzo-Indians, 94 Slavs, 88 Declined Queen's Gambits, 87 Najdorf Sicilians, 56 Kan Sicilians, 52 Classical Gruenfelds, and 49 Semi-Slavs.

Individual players find different openings logical. Since have more experience of Taimanov,4...Nc6 find this more logical than 4...a6. As Delchev notes can make a high class, independent rep with 4...Nc6. Instead if stick to 4...a6 have to be prepared to play some somewhat inferior lines in some places, despite what db stats say. (Taking seriously stats on move 4 is a pretty pointless exercise anyway. )

Optimissed has an individual take on 2...a6 3d4, which seems to be based on not liking e5 positions much. For most people e5 positions with activity to compensate weak structure  have been common sicilian position types for a long time. Players like Hou, nearly FIDE 2700  and Rapport FIDE 2700+ are still playing the e5 approach.

Not sure how relevant top ten play with their risk free wall approach as black, and avoiding main-line theory as white is relevant to club player play. Myself get more effective results if can put my FIDE 2000 level opponents under pressure in the opening, rather than waiting to later in game to try to do something. Again this is just my individual point of view. Opening play is mostly about what works for you, and making your individual biases as effective as possible.

This is going some way of OP's topic,  but personally think e5 setups are easier to play because central pawn structure determined early and for sometime. Also get fair share of centre. Kasparov was one of the best exponents of e6, d6 small centre. Very few of the present top 10 would subject themselves to the type of attack in game he first became World champion. Delchev in his books on Taimanov advises avoiding playing d6, leading to that type of centre, if at all possible, because difficult for black to play, and white has dangerous attacking possibilities. 

Sure, some players feel more comfortable in the ... e6 lines, others in the ... e5 lines. I like playing with the e6/d6 duo, but then I don't face the same opposition that Kasparov or Anand face. At our level, the objective soundness of a line is not the main factor in determining the result of the game.

@Optimissed:

The Kan? Difficult to play? It's one of the easiest mainline Sicilians to learn, relatively speaking.