Okay, but you didn't ask about a specific machine, so it wasn't a specific answer, just a general concept of why the 3J is usually smaller. You'll probably be fine with an 8" 3J but that's probably the max you'd want to try.
I'm sure different companies have different theories on what size chucks are best for their machines. It seems pretty common for modern 12" lathes to come with a 6" 3J as standard and most companies don't seem to put 8" 3J on until the 14" models.
I actually liked a 6.5" 3-jaw on my 14" Logan best of all for most normal work. The machine seemed a touch smoother, there was less chuck to work around and it was a lot nicer to take on/off. I had 8" 3J and 6J and 10" 4J chucks for it, but didn't use them if I didn't have to.
For my 16" Victor I've got 8" 3J, 8" 6J, 10" 3J, 10" 4J, and 12" 4J....I'm honestly thinking about getting another of the 6.5" 3J for it like I had on the Logan. Set-true style so it was super accurate and so much nicer to take on/off!
