Which is the correct method of coding eccentric reducers

My recommendation is to code a pipe element of the proper length, but average the diameter and wall thickness (of the connecting pipes). You can apply SIFs at the ends if desired.

There is one school of thought which says that for coding eccentric reducers, half of the length of the reducer should be of larger dia and related thickness, other half should be of smaller dia and thickness, and the eccentricity should be coded as a rigid element connecting the two halves and with properties of larger dia and thickness. Is it correct ?

Yes, this is another way some people model reducers. This method should be fine also.

I find that it is usually not worth while to code the vertical rigid element. The elevation change is quite small. Other than making the model look pretty, for the typical one size reduction it is not worth the trouble.

Now, when process decides that it would be a fine thing to put a 20x10 reducer on a pump nozzle, I'll model that will several step downs. Thankfully, that's only happend to me once and I think there was ultimately some flogging involved when it was discovered that that 20x10 reducer couldn't be bought.