The Four Pawns Attack is the most testing variation for white in the Alekhine Defense. White doesn't feel like sharing the center and grabs loads of space. In the process, white won't be as quick to get his pieces out which gives black time to weaken white's center and attack it from the sides. Neither player is safe in the Four Pawns.. 5. ... dxe5 6. fxe5 Nc6 is the main line and it's good for white but does gives black his usual chances.
The continuation with 7. Be3 is best for white, black will go queenside giving white a chance to start some sort of attack (a4-a5, Nb5, move the queen over etc) provided he can stop black from blowing up his center. Black can move around in modern style, play for f6, hit that d4 pawn so white shouldn't daudle. There are lines where white castles short, plays Nf3-g5, Rxf7 followed by Nb5.. in truth I think white's position should technically be excellent in this Four Pawns Attack, but it's so hard not to miss some weird move, some strange idea that guarantees black equality that it's tenable for black.

As for the Ilyin-Zhenevsky (which if I recall arises after the further 7. Nf3 Bg4 8. e6 fxe6 9. c5), it's not my cup of tea for white. I haven't seen it much with black in the many Alekhine defenses I've played, wouldn't mind it with black, I like black's resources. White has too much to do at once to have much of an advantage if black plays well. For instance, he should hold his c5-d4 pawns in place, prevent a favourable e5 break and deal with the pin on the Nf3.. that should slow white down enough so that black can get his ducks in a row and equalize. If black goes queenside, that could potentially be dangerous after some idea involving Qa4 (assuming the Nb6 maneuvers to f6).. I'm not sure what white should be planning in particular, shake the tree a bit so apples start falling off perhaps.