Being at the ground today, they were poles apart. Bracewell bowled into the wicket for long periods of time; Southee did it for 2-3 balls max.I hope Southee gets a bowl tomorrow at the last 3 wickets. Would be good for him to get amongst them. From what I watched Bracewell is out bowling him at the moment. Both of them, ostensibly, are similar in that they are outswing bowlers. Bracewell however has the better off cutter of the two and seams to get more seam movement in general.
I hope the competition amongst the seam bowlers is the making of Tim.
Bracewell hits the bat harder, as you said bowls a better off-cutter (ask Michael Clarke), is mentally tougher and can work to a plan much better.
I don't think it would matter a jot if Southee got the last three. I don't think he believes he can get top-class batsmen out anymore in Test cricket. And with an average climbing well over 40, he's probably right.