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If it were that simple the advance would be more popular - truth is Black has plenty of resources in this line, it is a very tricky line - White often pushes his pawns up on the kingside only to find his own king in trouble as Black usually goes 0-0-0. Added to this there is the standard queenside infiltration maneouvres.
Interestingly Sveshnikov himself in a recent New in chess says that ...c4 is Blacks best move "with a complicated game" but adds that the blocked positions are not to everybodys taste, which is certainly true.

Yes I agree delaying ...f6 is a very interesting way for Black to play in this ....c4 line. You need to have a certain mindset to play these blocked pawn chain positions but they are playable although theoretically maybe White is a tiny bit better there is plenty of opportunity for the better player to win.

It is an interesting decision which line to play as Black.

Yes, Klick I do know about the game. Don't you think Vallin missed the right move? After 8.Nh4!? g6 9.f4 fxe5 10.fxe5 Bg7?? and  falling for the eventual book trap. Why not 10.fxe5 Nh6!? The idea is to strong-point d6 with the Knight going to f7 or f5 and to encourage the Bxc4 sac . The knight moving twice for Black is justified.  White must eventually move his Knight. Now, Black has the option of moving the bishop to three squares. If Black prevents the c4 sac, the position looks equal with lots of play for both sides.

I also know that published games for 8.Nh4 is tremendous for White, but I just don't see an outright refutation for White.

Finally in caveat to Klicks comment about 6....Nh6, you miss a move you lose.  The true French player will take the backward pawn at e6 but not in conjunction with the doubled h pawns.

Why not 6...Nh6 over 6...c4, as the first leads to dynamic equality?

I think this is a really interesting question, and the answer probably depends on your personal preference, although I do have a move order comment to make.  Watson chooses 6...Nh6 as his main recommendation in Play the French (3rd ed.), saying that 6...c4 is holding up well but is less flexible.  Psakhis looks at both 6...c4 and 6...Nh6 (among other sixth moves) and seems to think both moves are in good shape theoretically.

My move order comment is this: if you want to play Pc5-c4 as Black after Pa2-a3 in the Advance Variation, it is possibly more accurate to avoid/delay Qd8-b6 and play Bd7:  that is, 1.e4 e6 2.d4 d5 3.e5 c5 4.c3 Nc6 5.Nf3 Bd7 6.a3 c4 is better than the position you have reached with the Q on b6 rather than the B on d7:

           "Incidentally, I think this way of playing [i.e.,
            responding to 6.a3 with 6...c4] is better after
            5...Bd7 than after 5...Qb6, since the b6-square
            remains free for occupation by the king's knight.
            This will greatly facilitate Black's ideal of
            establishing his bishop on a4."  - Psakhis

I actually really like the c4 move in the 5...Bd7 variation, as does Psakhis, who calls it "my favorite move."  (The more I look at the Psakhis trilogy on the French the more I like it.  There are many insights such as the one quoted above hidden in the notes.)  The center pawns are very static, the board is "cut in half" with Black and White castling on opposite sides, and the games in this line often feature slow buildups by Black and White on the sides that they castle.  In this line the really sharp tactics tend to arise later in the game after a period of prolonged manoevering.  This to me is a "classic" French position, one which is surprisingly rich in ideas (the slow but wonderful Bc8-d7-a4-c2-g6 manoever is just one such idea).  Black's play is somewhat dogmatic but very principled also.  In this line,  strategic understanding is probably the most important factor in your success.

Of course, the 5...Qb6 and 6...Nh6 line is also perfectly respectable, leading to a position which seems somewhat more tactical and dynamic (although not necessarily more interesting, there are some really great games in the 5...Bd7 6.a3 c4 line!).  So I guess it is really all a matter of taste in the end.   

      -Geof

My move is 6...Nh6 as it gives more chances to counter attack. But I will not state that this move is better than 6...c4. I think it is a matter of taste.