Is there an advantage of using a 30 size spinning reel over a size 20 for example?

Both casting distance and line pick-up rate of the larger diameter spool, especially if the frames are the same size. 

 

e.g., Shimano makes one 2500 on their 1000/2000 frame,

the other 2500 models and the 3000 models share the medium frame. 

The stroke is the same within each frame (small and medium), but the spool diameters increase on the larger model numbers that match each frame.  

 

You also gain reduced line memory with larger diameter spool. 

2 hours ago, NavyVet said:

Is there an advantage of using a 30 size spinning reel over a size 20 for example?

Higher IPT and better handling with larger line.

Would it be then that if you were using the same size diameter line, you could expect a greater casting distance and faster rate of retrieve  with a 3000 as compared to a 2500 spinning reel?

Yes, while a few mm won't make a huge difference, the line should leave the larger spool with less friction. 

 

Note that both of these spools are made for the same line diameter - the big 74-mm diameter surf/tournament reel is all about casting distance. 

Both spools were made for 8-lb test mono or PE#1.5. 

(The PE#1.5 is 35-lb test in the highest-strength braids)

 

8 hours ago, NavyVet said:

Would it be then that if you were using the same size diameter line, you could expect a greater casting distance and faster rate of retrieve  with a 3000 as compared to a 2500 spinning reel?

Yes, but with the caveat of "all other things being equal".