Which strategy to follow in the Modern Defence?

Although many people playing Black in the Modern Defence tend to play ...Nf6 after ...d6, (according to a database) to turn the game into a KID game, it seems that playing ...a6, maybe a ...Nd7 (perhaps delay it?) followed by a ...b5 and a ...c5 scores pretty high.

Is it advisable to go the KID route via ...Nf6, or is advisable to go the queenside pawn storm route via ..a6, maybe an ...Nd7 (or you could delay it), a ...b5 and a ...c5?

Example of the queenside pawn storm I'm talking about:

I don't know much about these lines but it can't turn into a KID until c4 is played. Black has independent lines after for example 4c4 i.e 4...e5, but again don't know much about them.

Ahaha Defence 666 (g6-d6-a6 = 666)

Also, it seems that the b5 pawn push is so devastating that White commonly plays a4 to prevent it from happening.