astrosoup, I take it you didn't have many luxuries and you had some troops defending your cities. Those troops are used as military police, "MP", to make content citizens. By switching to republic, you go from 2 MP max (despotism) to 2 mp max (republic). Going for monarchy does the opposite: you get 3 max. F3 tells you how many units you are allowed, and the cost of unallowed, extra units
Also, it is very recommendable to wait until you have a couple (2-3 on a tiny map, up to 7-8 on large) size 7+ cities, so the republican military support doesn't kick you in the balls. Reason for this is you are allowed 4 units per town in despotism, whereas it is one only in republic for each town 1-6, 3 for towns 7-12.
Given those, if you have a large military, it will cost you gold in republic. Also, they cannot be used for happiness, and thus you will need to pûsh up the entertainment slider a couple %'s. Combined, those factors can destroy all the purpose of going republic: getting rich.
Next time, try securing more luxuries and have a few towns besides rivers and lakes. Those will grow up to size 7 or 8 by the time you get republic, making up for the military support limit. When you don't have to worry (too much) about luxuries and unit support, AND if your worked tiles are all roaded (for extra gold income), republic will be your best friend and you will always be reluctant to go monarchy again.
If you cannot secure luxuries and/or have no river and lake nearby for big cities, consider monarchy as a good bet.