Seems to me like you'd want to go first... because at most, you get 3 attempts... and by going first there is always a chance you don't die on each one of your attempts, whereas by starting 2nd, you end up at 100% chance of death on your 3rd try... plus your odds are technically better for each one of your attempts if you are 1st...

1st attempt: Player A 1/6 die, Player B 2/6 die
2nd attempt: Player A 3/6 die, Player B 4/6 die
3rd attempt: Player A 5/6 die, Player B 6/6 die

Although, I'm not exactly sure that is a mathematically sound explanation... perhaps it is more of a "gut instinct" answer??