Both had nice games. My favorite were Mw2 and World at War

lol thats true
What will CoD Ghost go up against? Black Ops 3 vs CoD Ghost

Treyarch and Infinity Ward don't have a rivalry really, yeah it seems like that but you never see any of them hate each other's game. They aren't enemies in the Video Games industry.. They work for the same big company called Activison, so yeah I can see what you're coming from, but actually no rivalry is there.

They already do that, sharing assets and resources is a reason why Treyarch use the same engine as IW. Not just for cutting costs but it makes it easier to share stuff.
We know they share matchmaking information between the studios. As for the art team if I had to guess I would say a couple of them do work on both games at once. Makes no sense to have two art teams and one doing nothing the other is busy. Are parts of the cycle in which certain teams are less busy compared to the other art team for example are working on the DLC 6 months before release.
Treyarch for example are working on the new ghosts for the Wii U all them spare programmers come in handy

Alot of people don't understand the rivalry which is less them fighting more tying to a great series together. Pushing each other in creative ways along with helping.
World is not always black and white.

Maybe if the companies worked together, we could see some diversity within the series. I'm not sure though, I just think the franchise is so dead that nothing will help resurrect it above the Battlefield series.