I will disagree. 9" & 12" are so close to each other I wouldn't 't buy both unless you are planning on a ton of digging or just have excess money to spend. If you plan on using something larger than a 4x4 then get a 12" but if not get a 9". I have a 9" and 18". The 9" has worked for the hundreds of fence post holes I have dug and the only time I have used the 18" on fencing was for setting some 6.5" pipe for an entryway. Other times it just gets used for setting sono tube footings, I-beams, planting trees, etc.
Don't misunderstand me 9" and 12" have their place and if you were doing a ton of fencing with a lot of small and larger fence posts then buying both might make sense but from what I gathered from your post the wasn't the case.
Good point, luckily I haven't ordered anything yet. Do you think 20hp PTO is capable of running a 18" auger though? That was my concern....