for me the time to switch depends on how many cities i got and what kinda terrain ive got
by far the biggest thing that determines my opinion is the pop lvls in the cities
generally an optimum pop 6 city under a despot will produce 12 food 9 shields and 7 commerce (this is assuming 4 mined grasslands, 2 forests and all of them with roads), this is before corruption of course and i ain't including speciall bonus like cattle etc..
an optimum size 12 will be 24 food 15 shields and 13 commerce (10 mined grasslands, 2 forests and all with roads)
this kinda production will generally get you things like archers in a couple of turns and horse/swordsmen in 3 turns
under non despot governments an average pop 6 optimized city will be 12 food 12 shields and 7 commerce (14 commerce for republic) consiting of 2 irrigated grasslands and 4 mined hills all with roads
pop 12 would be 24 food 21 shields and 13 commerce (6 irrigated grasslands and 7 mined hills all with roads)
course getting that many hills ain't easy im just pointing out some possible optimum cities
the big difference with despots and other governents is if you decide to use specialists
despots cities being unable to get 3 food from squares (i ain't counting special squares for this point) can only really manage one specialist, other governments can have 2 for pop 6 cities (2 mined grasslands and 2 irragated grasslands) and as many as 5 for pop 12 cities (6 irigated grasslands and one mined grassland)
this means cities outside of the core radius can be producing as much as 5 beakers (from scientists) or 6 gold (5 taxmen and switch production to wealth) and as they are specialists it ain't effected by corruption
combine these wealth producing cities with the ability to rush using gold and you can see that large empires can benefit from other governments
the only key part bout whether to switch is really the terrain as many times the terrain means you can't optimize your cities and hence have little to gain from switching governments for a while yet
by far the biggest thing that determines my opinion is the pop lvls in the cities
generally an optimum pop 6 city under a despot will produce 12 food 9 shields and 7 commerce (this is assuming 4 mined grasslands, 2 forests and all of them with roads), this is before corruption of course and i ain't including speciall bonus like cattle etc..
an optimum size 12 will be 24 food 15 shields and 13 commerce (10 mined grasslands, 2 forests and all with roads)
this kinda production will generally get you things like archers in a couple of turns and horse/swordsmen in 3 turns
under non despot governments an average pop 6 optimized city will be 12 food 12 shields and 7 commerce (14 commerce for republic) consiting of 2 irrigated grasslands and 4 mined hills all with roads
pop 12 would be 24 food 21 shields and 13 commerce (6 irrigated grasslands and 7 mined hills all with roads)
course getting that many hills ain't easy im just pointing out some possible optimum cities
the big difference with despots and other governents is if you decide to use specialists
despots cities being unable to get 3 food from squares (i ain't counting special squares for this point) can only really manage one specialist, other governments can have 2 for pop 6 cities (2 mined grasslands and 2 irragated grasslands) and as many as 5 for pop 12 cities (6 irigated grasslands and one mined grassland)
this means cities outside of the core radius can be producing as much as 5 beakers (from scientists) or 6 gold (5 taxmen and switch production to wealth) and as they are specialists it ain't effected by corruption
combine these wealth producing cities with the ability to rush using gold and you can see that large empires can benefit from other governments
the only key part bout whether to switch is really the terrain as many times the terrain means you can't optimize your cities and hence have little to gain from switching governments for a while yet