Would you allow Pirc or King's Indian?

Would you allow the Pirc by playing 2. e4? Or would you allow the King's Indian by playing 2. c4?

If we're just examining this choice in isolation - I would choose a KID just because the positions are more fun and complex. If my goal were to win at all costs, I would go for the Byrne variation of the Pirc which will just land you a 70% winrate. But in general the positions in the Pirc are cramped and maneuvering, you don't get the two sides of the board positions and space advantages as in the KID due to Nc3 blocking the c pawn, and I find the Pirc positions are not very enjoyable from either side. The Byrne bypasses alot of theory with an early attack though. But against the Modern, or if they respond properly, you still have to play a typical Pirc.
But in reality, your repertoire dictates this - if you're playing a Trompowsky or Jobava, which avoids the KID and can transpose with a Pirc, you'd choose the Pirc. If you're playing c4/d4, which faces the KID after Nf6 g6, you would play a KID here.

Neither!

I lay the choice back on Black - King's Indian, Old Indian, or Old Benoni.

1.d4 d6 2.e4 Nf6 3.f3

Now 3...e5 will lead to a Saemisch Old Indian, 3...g6 will lead to a Kings Indian, and 3...c5 4.d4 without c4 will lead to an Old Benoni.

The problem with 2.c4 is 2...e5!