basically the "SE" is just specialist economy which means for the most part you rely on specialists instead of cottages. now with a SE if your like me its more of a hybrid since you want your money making and science producing cities to have "some" cottages for added effectiveness since its quite easy to max out those specialists (merchants and scientists, unless you run CS, but if you ask me running serfdom allows to build many farmlands faster since on average your cities running SE tend to grow faster and you want those citizens only working developed tiles so you can run more specialists and have a higher production like i like to do). another requirement of running the SE is to have the pyramids early so you can run representation gov't for the added +3 beakers per specialist since you'll have fewer cottages this will offset the lack of science and if your good and get some big cities capable of supporting alot of specialists sometimes your science can be higher running a SE as compared to a CE. there are also some other wonders that help alot such as Angkor Wat which gives priests an extra hammer and using them adds gold too, most effectively used with two or more religions. the sistine chapel makes winning via CV (culture victory) very easy running the SE.
generally running a good SE will allow better production since you have more food to run mines and support priests/engineers while having sometimes ridiculous GP (great person) rates throughout from all those specialists (parthenon is very good to get with this approach) whereas running the CE you wont get as many GP.
both approaches have their pros and cons but in my opinion especially once you get biology SE can and should be (if you planned accordingly) far better than a CE. running a SE requires alot of grasslands and fresh water and if your scarce on those two (food resources too) you might want to consider running a CE.
i think i covered it all, if not just ask.