Teletubbies will win. They have the Noo-Noo, after all–he/she/it (?) has always come to their rescue in the past. The Noo-Noo will suck Barney into its body, and then the Teletubbies will chase it around shouting “Naughty Noo-Noo!” over and over again.
Then the Noo-Noo will spit Barney back out, and the fight will begiin all over again, and again, and again…
Where and when is this match to be held?
How long does it take to program a cruise missile?
Everybody involved in this fight is made of foam rubber, so blunt weapons & pummling are useless.
Time to break out the knives, kiddies! 
While they are fighting, Barney and the teletubbies get blown up. If you are wondering what happened, I had Barney eat some explosives.