The situation I had was player A played a dead Upset card and Player B played a +5 dead energy card.
Player B had the better team stats so in a normal dead vs. dead would have won.
Who won the contest in this case? (I couldn't find anything in either rulebook to help)
It's in the rules (though I don't have access to the new ones atm). It's under resolving dead cards. If both of you played dead cards they count as +0, and you look at the team stat. If that's also +0, then you'd tie and the active player would roll the tiebreaker die.