Hi Mike,
I used a 12" auger on my 4"x4" posts and and 6"x6" posts. In many cases, having the "extra space" was very handy in case the hole wasn't exactly in the right place.
Also, you need to remember to measure the diameter of the posts rather than the side dimensions. A 4"x4" post is actually about 3.5" x 3.5" and has a diameter of almost 5". A 4"x6" post is actually about 3.5"x5.5" and has a diameter of about 6.5". So, a 6" bit wouldn't help at all for 4"x6" posts, and would just barely work for 4"x4"s.
I think I'd use at least a 9". Again, my experience in my rock hard and rock filled clay is that the bit can wander a bit, so I really liked the extra room the 12" bit gave.
Hope this helps.
Rick