What do you mean when you say monarchy? Is it an absolutist or constitutional monarchy? If it's a constitutional monarchy, then is it elective or hereditary? And what exactly are the attributions of the monarch: is he/she just a figurehead or does he/she possess more substantial power? If he/she possess more substantial power (i.e. making or approving laws, conducting diplomacy, declaring war etc) then what are the mechanism that keep him/her in check: is there a Parliament to do this? And so on.
Same with the presidency. Is it a democratically elected president or self-appointed (or worse, appointed by a foreign power)? If he's democratically elected, is he directly elected by the people or is he elected by the Parliament? How much power does he poses in comparison to the Parliament: is it a parliamentary democracy or is it a presidential democracy?
You can't really compare the two if you're not taking into consideration all these questions. OK, I suppose you could come up with something like "Power to the people, f*ck hereditary privilege," but that would be quite a shitty essay, frankly