No, the Pirc/Modern and the King's Indian Defense are nothing alike! Just because Black fianchettos a Bishop in both doesn't make the play similar. There are 32 pieces, not 16.
Your best bet is the French Defense. Like the King's Indian (which I play both in OTB tournaments - KID and French), you get a blocked center more often than not, and just like in the King's Indian, the pawn pointing theory comes into play.
When the center is completely blocked, look to see which way the blocked pawns are pointing. That's the side you should be attacking.
So, for example, in the Classical KID, the blocked center sees the White pawns pointing towards the Queenside and the Black pawns point toward the Kingside. Therefore, Black attacks Kingside and White attacks Queenside.
If you look at the French, it's the same concept, except in this case, it is Black that's attacking Queenside and White Kingside.
As white I can play KIA which I have lately adopted, what would be the most king's indian like defense against 1.e4? Would it be something like the Pirc, Modern or something like that. Please help me find a good defense against 1.e4.