Hi,

There are various types of radio models which are available in the market. But broadly they can be classified as computerized and non-computerized radios. What I would like to know is: Which feature set(s) are missing in the non-computerized ones and does the absence of these features affect flying capabilities.

I think these threads would get you very close to the answer.

http://www.rcindia.org/radios-and-receivers/what-radiotransmitter-features-are-important-to-you/

http://www.rcindia.org/radios-and-receivers/big-brand-radio-comparisons-with-others/

As a lay man language, and according to me, the major difference between computerized and No comp. version is flexiblity....
i have a build a LED controller with 26 different modes of lightning. the best part is that it uses minimal external components and that too only passive one. rest all is pre-programmed and built onto the micro controller itself. similarly, in computerized radio all features are pre-programmed on the micro controller itself and we have to select by giving some input, and out put can be seen on servos action, like dual rate, exponential setup.
The same thing can also be done using electronics components circuit but that will take a huge space and might not fit in your tx box/cabinet  . i also think that computer radio power consumption is much less then non computer radio.
In sort every action of your control stick, switch or pots is computed at a very good accuracy and out put is sent to your servos, motor or any other control electronics. this is primarily done by software programming which is embedded onto the micro controller of a computer radio.