When should white prefer a Maroczy structure vs. a Kings Indian structure?

Question

In two games quite different games that I played recently, I was playing white and had a very nice centre, but according to the engine I misjudged pushing (or not pushing) my d-pawn both times.

From my understanding of pawn structures, I could aim for a KID-type position by pushing d4-d5, or allow black to take on d4 for a Maroczy pawn structure. My question is simply how can I practically understand which is better?

[FEN ""]
[Event "Rated Rapid game"]
[Date "2022.01.20"]
[Result "0-1"]
[WhiteElo "2053"]
[BlackElo "2025"]
[TimeControl "900+10"]
[Termination "Normal"]
[UTCDate "2022.01.21"]
[UTCTime "07:12:31"]
[Variant "Standard"]
[ECO "C41"]
[Opening "Philidor Defense: Hanham Variation"]

1. e4 { [%clk 0:15:00] } 1... d6 { [%clk 0:15:00] } 2. Nf3 { [%clk 0:15:06] } 2... Nd7 { [%clk 0:15:05] } 3. d4 { [%clk 0:15:15] } 3... e5 { [%clk 0:15:08] } 4. d5 { [%clk 0:15:12] } 4... Ngf6 { [%clk 0:15:10] } 5. Bd3 { [%clk 0:15:18] } 5... Nc5 { [%clk 0:15:14] } 6. Qe2 { [%clk 0:15:13] } 6... Be7 { [%clk 0:15:16] } 7. b4 { [%clk 0:15:15] } 7... Nxd3+ { [%clk 0:15:19] } 8. Qxd3 { [%clk 0:15:24] } 8... a5 { [%clk 0:15:21] } 9. bxa5 { [%clk 0:14:29] } 9... Rxa5 { [%clk 0:15:21] } 10. c4 { [%clk 0:14:34] } 10... Bd7 { [%clk 0:15:21] } 11. h3 { [%clk 0:14:37] } 11... Qa8 { [%clk 0:15:28] } 12. Nc3 { [%clk 0:14:28] } 12... O-O { [%clk 0:15:04] } 13. O-O { [%clk 0:14:34] } 13... b6 { [%clk 0:14:57] } 0-1

(This was bad for white)

[FEN ""]
[Event "Rated Classical game"]
[Result "1-0"]
[WhiteElo "2024"]
[BlackElo "1886"]
[TimeControl "1800+0"]
[Termination "Normal"]
[UTCDate "2022.01.21"]
[UTCTime "07:15:07"]
[Variant "Standard"]
[ECO "E90"]
[Opening "King's Indian Defense: Normal Variation, Rare Defenses"]

1. d4 { [%eval 0.3] [%clk 0:30:00] } 1... Nf6 { [%eval 0.0] [%clk 0:30:00] } 2. c4 { [%eval 0.23] [%clk 0:29:59] } 2... d6 { [%eval 0.51] [%clk 0:30:00] } 3. Nc3 { [%eval 0.65] [%clk 0:29:56] } 3... g6 { [%eval 0.53] [%clk 0:30:00] } 4. e4 { [%eval 0.68] [%clk 0:29:54] } 4... Bg7 { [%eval 0.59] [%clk 0:30:00] } 5. Nf3 { [%eval 0.7] [%clk 0:29:48] } 5... O-O { [%eval 0.48] [%clk 0:29:59] } 6. h3 { [%eval 0.32] [%clk 0:29:39] } 6... c5?! { [%eval 0.89] } { Inaccuracy. e5 was best. } { [%clk 0:29:58] } (6... e5 7. d5 Nh5 8. g3 f5 9. exf5 gxf5 10. Ng5 Nf6 11. g4) 7. Be3 { [%eval 0.72] [%clk 0:28:50] } 7... Nc6?! { [%eval 1.37] } { Inaccuracy. Qa5 was best. } { [%clk 0:29:44] } (7... Qa5 8. Bd3 cxd4 9. Nxd4 Nc6 10. O-O Be6 11. Be2 Nxd4 12. Bxd4) 8. Be2?! { [%eval 0.45] } { Inaccuracy. d5 was best. } { [%clk 0:28:36] } (8. d5 Na5 9. Be2 b6 10. Qc2 e6 11. O-O e5 12. Nh2 Ne8) 8... cxd4 { [%eval 0.87] [%clk 0:29:42] } 9. Nxd4 { [%eval 0.83] [%clk 0:28:35] } 1-0

(This was fine for white, but apparently pushing d4-d5 as annotated was better).

Answer 1

[FEN ""]
1. e4 d6 2. Nf3 Nd7 3. d4 e5 4.Bc4 Be7 5.O-O

Keep the pawn on d4, because Nf3xd4 gives you a strong knight on d4.

Keep the d5 square free for a Nb1-c3-d5 jump.

Also, to keep the a2-g8 diagonal open for the light squared bishop.

You might tuck the bishop away with a2-a3 and Bc4-a2.

Play a Rf1-e1 and h2-h3 setup.

Sometimes Nb1-d2-f1-g3 or -e3 can be interesting.

[FEN ""]
1. d4 Nf6 2. c4 d6 3. Nc3 g6 4. e4 Bg7 5. f3 O-O 6. Be3 c5 7. d5

When placing pawns on light squares, make sure your light squared bishop stays useful.

Here, d4-d5 stops Nb8-c6-d4.

It also keeps the position closed, which is good, because the king is still on e1.

You might attack with Qd1-d2, g2-g4, Ng1-e2-g3, h2-h4-h5.