I have so far played either as an absolute (Maratha) or constitutional (GB) monarchy. I prefer constitutional monarchy. Research goes at a decent pace, I can get rid of bad ministers, and most importantly, industrialization does not cause clamour for reform.
This last one allows me to upgrade all my territories to the max, with only a token garrison - if any.
I'm not sure what additional benefits a republic brings that would make it worth to have unsackable ministers.
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