Dice must match the die reference face on the bottom of the card for tournament play.
Sometimes there will be slight color variation within a set (ie the 'redness' of Red Hulk's die isn't identical to the red of the card). Those dice are obviously still okay for use. However, despite having the same stats, you couldn't use the green Hulk die from Avengers vs. X-Men on your Red Hulk from Uncanny X-Men (nor could you do so on cards that have the same name like Wolverine or Captain America).
This is now covered under the Tournament Rules:
http://wizkids.com/dicemasters/tournament-rules/-The Dice Masters Rules Team