Over a long period of time Kasparov's theroy seems like it would stand. I would imagine it is more-so for titled players as they make fewer and less serious mistakes that non-titled players.
Winning a 9-round tournament probability with a certain style

I mean, rating (if it's accurate, and once you get your over-the-board rating going it's pretty reliable; ratings here at chess.com? Not as much!) is ultimately the most important factor as that more than style determines the winner. There are of course many small intangible factors too like physical condition or general mood, and some people find an easier time playing against certain styles compared to others, but I wouldn't worry too much about those. Chances are, a 2000 will beat an 1800 most of the time, who will beat a 1600 most of the time, and so on, regardless.
Still, I've heard that at the highest level the more cautious players have problems winning tournaments because, as they want to build their position within reason and safety, but perhaps not play too overwhelmingly, their opponent is probably good enough that they won't often make an unforced error, and they get too many draws. Compare that to playing more aggressively: there's a lot more potential for a win. Losses too yes, but someone who is aggressive and simultaneously in good form will probably get the most points.
In fact, I've seen old tournament records involving players like Alekhine, Nimzowitsch, Capablanca, etc, and I notice that there can be some players who lose just one game (or even none!), out of like 16 games, yet aren't even close to 1st because they have too many draws. I've heard Petrosian had this problem with tournaments as he played so safely.
However, at most other levels, slow play is probably as good as anything, as in fact it may provoke the opponent to be too aggressive at the wrong moment and totally ruin his position beyond repair. Since unforced errors often are made, often in comfortable positions even, it probably does balance out decently enough.

Logically the "aggressive" player should generally win more tournaments as they have the chance to go extremely positive or extremely negative. Thus in a long tournament the decisive players will place more at the top and bottom.

Thx for running buy, Elubas! I played in a 9-rounder U2000 national championship and top 3 winners were:
1st place: an underrated(1900 elo but 2040 fide) grown up person with "I love running" written on the t-shirt. - 7 points.
2nd place: 1880 fide, a 15 year old who played so passive that got 5 draws, 4 wins. - 6.5 points.
3rd place: in late 20th, 1830 fide, aggressive style. good physical shape. 2 loses, 1 draw, 6 wins. -6.5 points.
Winner nr.1 makes sense that he won he played positionally and was the highest rated and in good form.
Winner nr 2. if he did`t win and drew last game(would`be been 6 draws!!! gez how boring.) he would not reach top 3.
Winner nr 3. Turned two lost games into a draw and a win. "Victory favours the brave"?
So nr 2. and 3. luckily had their unique portion of luck.
I was nr. 3 and playing aggressively I think takes much more energy than playing passive. I pumped muscles twice: once before tournament and once after the 5th round when I felt energy is leaving me. Also I feel that purely strategically, playing aggressively in U2000 (!!) group has less chance to come in top 3 compaired to passive-styler in a 9-rounder.

Logically the "aggressive" player should generally win more tournaments as they have the chance to go extremely positive or extremely negative. Thus in a long tournament the decisive players will place more at the top and bottom.
U2000 skill is low to play aggressive. the one who tries to win a game puts him self at risk of falling for many "sins" of U2000 skilled players like "attention distribution".
I would guess that in the long run, their average finish would be similar, but the aggressive player would have more wins (and more very low finishes).

Logically the "aggressive" player should generally win more tournaments as they have the chance to go extremely positive or extremely negative. Thus in a long tournament the decisive players will place more at the top and bottom.
U2000 skill is low to play aggressive. the one who tries to win a game puts him self at risk of falling for many "sins" of U2000 skilled players like "attention distribution".

I would guess that in the long run, their average finish would be similar, but the aggressive player would have more wins (and more very low finishes).
This.
Also, the aggressive player tends to do better in tournaments while the defensive player would do better in matches.
That's because in a match a drawn game maintains your current position (your opponent also gets only 1/2 point, just like you), while in a tournament a drawn game tends to erode your competitive position since one of the other players will probably defeat his own opponent, scoring a full point and pulling a half-point ahead of you.

One needs to have a lot of stamina and courage to play a 9-round chess tournament. so don't tire yourself out by playing games during break, because one needs the energy to play the chess game itself. Don't lose hope when you lose one or two games, because the champion is not the one who leads at the beginning nor the end, but at the end.
Player A plays in a defensive style (1.d4 2.Bf4 3.c3 as white and Phillidor defence kind of set-ups as Black).
Player B plays aggressively -(1.e4 and opening f-file, open games and things like that & as black sicilian and some aggressive stuff vs. d4 as well).
Who has the highest probability to come in top 3 in a 9-round long tournament "U2000 fide" and who has in a "closed 2000-2200 fide" ?
I know Kasparov said that style does not matter because defender will draw more, aggressor will lose more but win more than defender so it gets balanced "at the end of the day". But I think he was talking about titled players.
So, did anyone actually tested/checked this and knows for sure?