Frankly I feel like the french defense can attempt to take center control faster than the pirc can
French Defence or Pirc Defence ?

I am a big French fan which you can learn more about in my French study.
The Pirc is something I love to face even as a d4 player because of this very high probability trap. I will only show the trap and allow you to do your own work for the best continuation
This even worked against a GM on Lichess so it still has venom and is even more lethal if you transpose into a Pirc from d4 as this doesn't work against the King's Indian

I am a big French fan which you can learn more about in my French study.
The Pirc is something I love to face even as a d4 player because of this very high probability trap. I will only show the trap and allow you to do your own work for the best continuation
This even worked against a GM on Lichess so it still has venom and is even more lethal if you transpose into a Pirc from d4 as this doesn't work against the King's Indian
I suppose you learnt this trick from Jonathan Schrantz's popular video. This is what I play against the Pirc now as well, mainly due to Jonathan's video.
Fun fact: when I played him on lichess Johnathan fell for his own trap and resigned against me on move 9

Of course this "trap" is nothing, actually after 5.e5?! Nfd7, Black is already totally fine.
Obviously 4.Bg5 is far from being the most testing setup against the Pirc, and even 5.e5 is probably inferior to a simple 5.Qd2 (as recommended by Lakdawala) but I still like white in these lines.
5.e5 Nfd7 6.exd6 cxd6 7.Qd2 h6 8.Be3 Nf6 9.h3 Nbd7 10.Nf3 a6 11.a4 is analysed as slightly better for white in FM Plichta's chessable repertoire, and I agree.
7...0-0 is met by 8.h4! and I think black's position is already very difficult to handle for human players.

I'd like to know why after 1. Nc3 Nf6 2. e4 black didn't play d5 to transpose to the awkward variation of the declined Aljechin?

The Byrne variation discussed above is indeed tricky for the unaware but not a big problem. I’m surprised nobody has advocated the Austrian Attack which is very dangerous. There is another line where White plays quietly with an early a4 and h3 that takes the sting out of the Pirc. A number of people have mentioned similarities of the Pirc to the King’s Indian. I do well with the Pirc but have a lot of trouble with the KID. Anyhow, as one who has converted from the French to the Pirc this has been a useful discussion.

French defense by far. Teaches you about pawn play and maneuvering, two skills I think many people neglect.
In the '70's I played Pirc-Modern for a while after being inspired by the bizarre games of Suttles. I had a series of bizarre games of my own against strong players where we didnt know till the end who was winning. I finally dropped it when I got crushed in a game and couldn't find a significant improvement. (I switched to the Schliemann which was easy then because everyone played the Ruy Lopez vs 1. e4 e4.) If you want a defense that is fundamentally sound so that when you lose you'll know it wasn't the defense it was how you played it, I'd say try the French & see if it 'feels right'.

I implied that it was serious tournament games
I personally only play his setup in bullet; he doesn't.

The Pirc, if only because you don’t have to deal with the French Exchange variation, the most boring line in the world.
That MIGHT be true

I like to transpose the Pirc/Modern into the King's Indian Defense, because I know a lot of KID theory as white
SAME!!!!!

I think pfren's wisecrack was apt. Accurate play is required of all openings.
Pfren was absolutely right. The bottom line is that you have to know what you are doing. I was amused at the people who advocated the Byrne system trap. Yes, if Black makes the worst moves the Pirc is awful. But what happens when Black knows this simplistic stuff and White’s one trick strategy failed? Then White is wondering, Duh, my trap didn’t work so now what?

I think pfren's wisecrack was apt. Accurate play is required of all openings.
Pfren was absolutely right. The bottom line is that you have to know what you are doing. I was amused at the people who advocated the Byrne system trap. Yes, if Black makes the worst moves the Pirc is awful. But what happens when Black knows this simplistic stuff and White’s one trick strategy failed? Then White is wondering, Duh, my trap didn’t work so now what?
So now you play a somewhat equal position. Since I usually get minus positions out of the opening, I’d take a nice equal position if I can.
I think the French is the better opening to choose. The Pirc is an extremely difficult opening to master because White's play is much simpler. For instance, White can play 1.e4 d6 2.d4 Nf6 3.Nc3 g6 4.Be3, 5.Qd2, Bh6 at some point and shove the h-pawn down the board, similar to what is played against the Dragon, and this attack is extremely dangerous because it comes extremely fast. I think for where you are at currently, the French will be more appealing.
Although there is this joke about the French (the terrible LSB), the French has an advantage that other openings don't in that Black is guaranteed to have a pawn in the center (i.e. d5).
But you can play the Czech Pirc and not have to deal with this. The 160 Attack that you recommend is dangerous but Black needs to counter with c6 and get the Queen out. Lots of White players think that the 160 is a magic bullet and get over confident but Black can counter it. Black needs to not freak out and avoid castling on the Kingside. I think the Austrian Attack is much tougher and extremely complex. Yasser Seriwan played the Pirc very well as Black.
My point is, I don't think it is appropriate for people at the OP's current rating to pick up the Pirc. It isn't a "KID against 1.e4" as most people may think. I am not denying that the Pirc is perfectly playable, but it has a pretty high skill cap.