Speed and aggression.

In the case of a tie in points in a Swiss-system tournament, the following are used in descending order:
1. Head-to-head result
2. Buchholz score (the scores of opponents are summed with weighted coefficients: 1 for a win, 1 for a draw, 1 for a loss)
3. Sonneborn-Berger score (the scores of opponents are summed with weights: 2 for a win, 1 for a draw, 0 for a loss)
"Wikipedia" is incorrect in this case.
An important difference in the program: Berger distinguishes between a technical win and a regular win, which is why it was chosen.
In general, the coefficients do not reflect the real balance of power and are essentially a "coin flip." Ideally, an additional game should be played for the prize-winning places.

That's not true.

In Swiss-system tournaments, especially with a large number of participants, it is not uncommon for the winner and prize-winners to not play against each other at all, so the Buchholz score was chosen as the main criterion for Swiss-system tournaments. Previously, the progress coefficient was used as the next indicator after Buchholz, but now the average rating of opponents is mainly calculated. There is no head-to-head criterion in a Swiss-system tournament. The introduction of the head-to-head criterion and the Sonneborn-Berger score is already an initiative of individual people. The Sonneborn-Berger score is mainly used in round-robin tournaments (the scores of opponents are summed with weights: 1 for a win, 0.5 for a draw, 0 for a loss).
In round-robin tournaments, the first criterion is the head-to-head result, followed by Berger. Buchholz is meaningless because it is the same for everyone.

P.S. There are many resources on the internet, besides Wikipedia, where you can find the rules of the Swiss-system tournament.