Play caller
If you had to pick just one, I would go for a btter play caller (obviously a good referee is balanaced in oth - they are not mutually exclusive).
Here is my reasoning:
Say your "Play Caller" get 99% of the calls right, and has huge game management problems, while your "Game Manager" can manage the game, but only gets, say, 65% of the calls (or no calls) right.
When the play caller kicks a call (1%) there will probably be a game management issue arising. If need be his (or her) partners, referees supervisor or even players/coaches can help out with game management.
On the other hand, when the "Game Manager" kicks a call - there is nobody that can resuce the referee.
In a nutshell, game management can be helped by others - only the referee watching the play can make the call.
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