twin die d(6,6) vs. vanilla d12 -- which to reroll?

haven't done the math yet -- and it's probably pretty close -- but the tension to me is hat
the twin die rolls a little higher on average, but also is less likely to roll a "12".

Button Men Game #723466 
Tournament Legal challenge, copying communication from game 722199

Skills in this game: Twin, Reserve, X Swing

Player: ElihuRoot *Dead Dude* *Fanatic*
Your Button Man: Krosp (4 (6,6) 12 12 X)   Score: 42 (14.6 sides)   Rounds Won/Lost/Tied: 0 / 0 / 0 (Out of 3 wins)
Your Captured Dice: Twin Die (both with 10 sides), 4-sided die

Twin Die (both with 6 sides)	12-sided die	12-sided die		X Swing (with 7 sides)
9	5	10		3 Captured last turn
6-sided die	12-sided die
6	11

Opponent: theAlmighty *heavenly* *Silver Medal in Men's Basketball* *Silver Medal in Men's Fencing* *Silver Medal in Men's Judo* *Gold Medal in Men's Table Tennis*
Button Man: Cammy Neko (4 6 12 (10,10) r12 r20 r20 r(8,8))   Score: 20 (-14.6 sides)   Rounds Won/Lost/Tied: 0 / 0 / 0
Captured Dice: 4-sided die, X Swing 7-sided die