Ok, I have seen the 12 position LS-30 -type joysticks have a round yellow handle and some have an octagonal yellow handle?
1) Do the joysticks play the same way?
Yes! They will feel a little different, of course, but they both do pretty much the same thing.
2) Is there any advantage between one type over the other (ie: more reliable, sturdy, working better, etc..)?
Not that I know of, other than the look and feel of the grip. I don't actually own the Wico type, though.
3) Are both the round and octagonal joysticks made by the same company?
Nope. Octagonal ones are SNK LS-30s, which were actually manufactured by Semitsu. Round, barrel shaped ones came on Data East Machines, and were made by Wico. Wico also made a balltop model.
4) Can both types be used by Druin's interface board?
Yes! And so can the ones you may see with the black pear-top handle- those are the Happ varietiy, and the only ones you can still buy new. The others you'll have to score on ebay.