How exactly?
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Scoring systems that give proportionally more points for birdies and eagles favour long hitters that play aggressively, especially on open courses and/or where negative points for double/triple bogies are not part of the scoring system.
OTOH, scoring systems with only a one-point difference that start at bogie or even double-bogie favour conservative, straight hitters, since they can usually pick up at least one point on every hole. Aggressive long hitters are at a disadvantage then (especially on a narrow, tight course) because they can miss out on points with wayward shots and yet the reward for eagles is not that great.
The bottom line is that the tournament organizer often determines the scoring system, and in many club competitions the tournament organizer is also playing in the competition. That should be a concern.
Aggressive or conservative play is the players' choice. Aggressive play implies risk. Players must decide on their balance between risk and reward. Good long hitters don't have to be aggressive. Poor players trying to hit overlong are just poor players.
If a player doesn't like the way a competition is run, he doesn't have to play. But are Club Championships really run on the whim of one person?
Incidentally, I have never encountered a Club Championship played as a stableford.