The Leningrad is probably more flexible than the Classical Dutch, as c7-c6-c5 and c7-c5 are sometimes possible. You will not see this in the Classical Dutch. But I find the Classical Dutch easier to play.
The Stonewall is in my opinion very rigid.
Finally I think White can prove a solid edge against the Bb4+ systems (with Nd2) and the Alekhine Variation (with 7.Nbd2 Bf6 8.Nxe4).

The critical lines of the Iljin-Zjenevsky are definitely:
1.d4 e6 2.c4 f5 3.g3 Nf6 4.Bg2 Be7 5.Nf3 o-o 6.o-o d6
A) 7.b4 or 7.Nc3 Qe8 8.b4.
B) 7.Nc3 Qe8 (a5 8.b3 or Ne4 9.Qc2 Nxc3 10.Qxc3; I think 7.. d5 is inferior) 8.b3 and now Nc6, Qh5 or a5.
While the Iljin-Zjenevsky in general is a bit rigid, as Black focuses on e6-e5, he has a fair choice in B.

In almost all other White setups Black equalizes with either e6-e5 or Ne4. The only exception I can think of at the moment is 1.d4 e6 2.Nf3 f5 3.d5.
If you really consider playing 1.d4 e6 2... f5, then you should study the aforementioned two systems first. I only dared to play the IZ in email chess, when I had got confidence in Black's chances here.

It is my impression, that Black has more than two critical lines to face in the Leningrad, but I am not sure.