As a big SE player for a long time, I'd like to chime in here with a few thoughts that I didn't see covered.
A SE can easily mesh with the most powerful early game civic, Slavery, in that they both utilize Food as their main resource. The problem with the CE is that it takes time to grow to its max potential, where as a Farm takes X turns and is done, no more waiting. Sure the city may take time to grow, but a few early Farm-resources makes your city grow very fast.
Knowing that it takes active tile working time to get the Cottages to mature, once early cities are at their max sustainable size, I tend to hybridize. This means I may even stop working the Farm-resource to maximize future potental. Knowing that I may do this, during the early game I tend to keep my cities very close to each other, even overlapping a lot. This lets me have City #2 work City #1s Food resource once City #1 is done growing. Also, when I start whipping things, I could have City #2 work City #1s towns while waiting for the whipping unhappiness to wear off.
Proper spacing (read: overlapping) of early cities lets me utilize both Cottages and Slavery the way I used to Specialists and Slavery. This trick really gave my CE game a huge boost.
Now for a comparative taste of the SE vs the CE, it's all in the numbers.
A Post Biology Farm nets you +2 Food on that tile. Two food is equivilant to +1 Specialst. +1 Specialist is equivilant to 6 Beakers or 3 Gold 3 Beakers at best.*
A Post Liberalism Town nets you +7 Commerce +1 Hammer on that tile at best.*
*I am assuming the appropriate Civics are being run at this time.
One thing I'd like to note here is that you need far fewer +gold buildings in a Specialist Ecenomy, because you only need those buildings in the cities (city?) where you will be running Merchant Specialists. However, this is offset by the need for the SE to build more Health and Happiness buildings.
So if the SE is outmatched by the CE, why does anybody play the SE?
The answer is time and flexability.
The SE requires far less dependancy on both Civics and your Slider, which lets you be more flexable with many other aspects of the game. The fact is, a CE almost forces you into a single set of Civics predetermined by the game, where as the SE does not.
Since only one Civic is truly necessary for a SE, you can easily get away with running many fun civics for a lot longer than you could if you were running a heavy CE. Do you need more Scientist Specialists? Whip a new Scientist building with your Slavery Civic! Or you could do the peaceful thing and revolt into Caste System, but I prefer whipping if I'm going Food Crazy.
In many games I have tanked my Economy and been in the red at 100% Gold yet still trudged along in tech due to the SE's naturue. Also, If I ever feel that I need to defy a resolution or two in a SE I can! I simply tick up the Culture Slider a bit, and let the Theatres and Collesums keep my uppity citizens content. In fact, there have been a few games where I have turned down the Science Slider to turn up the Culture Slider and seen an increase in my science!
A few final things to note:
Look at the timeframe when a SE and a CE really shine
A CE is fully mature after Printing Press, Liberalism, and Democracy are learned.
A SE is fully mature after Biology.
Also examine the build-up to each separate economy.
Can you grow Towns before Free Speech and Universal Suffrage? Yes! This means that once your US and FS civics are unlocked, you can easily reap the full benefits of your Tows.
Can you grow your cities to the same size they would be post Biology Farms? No. This means that even after you tech Biology, which comes later than Democracy most of the time, you still have to wait for your cities to grow.
The SE also has diminishing returns in two ways, Great People and Growth Time.
The SE nets you Great People like you wouldn't believe. For a while. Then the number of GPP necessary to net the next Great Person gets so high, you may as well not be producing any GPP. In a CE, with one National Epic'd GPP farm, you can easily produce many Great Persons.
Growth Time is another factor that bears looking into. Post Biology, as you grow in size, the amount of time it takes to get one size bigger increases in a way you wouldn't believe. Since each city size takes more food than the last, and each time you grow one size bigger, your positive food is reduced by 2 (because that food is now being eaten by the new citizen) you will sometimes take 40, 50, or even 60 marathon turns to grow a city to it's final size.
Almost everything I have said are factors which have not been taken into account in the first post's comparison. A CE is much better than a SE in terms of pure tech, but a SE wins out in its ability to be flexable.