I think that if these two boys are so unenthusiastic about the activities they are doing that they resort to bickering for amusement, they must be pretty bored and unchallenged.
They need to be kept busy. What do you currently do for them that they could easily do for you? Hoovering, laundry, ironing, cleaning a bathroom within an inch of its life, cleaning the oven, dinner or dessert prep, gardening, changing beds and turning mattresses are all things able bodied children should be able to do at those ages. They are taking you for granted and abusing the spare time they have. They need to value it more and make the best of it when they have it. The way to do that is to take it away and make them earn it back. TV and games, etc., should be a privilege they earn for co-operation in doing chores and not something they can use as a prop for their fights. When they earn it back, maybe make it a family event?
Make their lives revolve around you if it doesn't already. You should be guaranteed a few hours a day when your children are too busy to bicker.
They should also be playing some sort of organised sport where they will have other children and coaches/teachers to knock some of their corners off. How about martial arts? Football? Swimming? Something to tire them out and give them discipline. I also recommend making a family effort to volunteer for the needy as a way of getting children outside of themselves.
Old habits may die hard, however, even when trying to work together on chores, and when they come to you with tales, tell them you are not interested and to carry on until one of them is seriously hurt, and then deal with that themselves too. Seriously, do not try to sort out who did what, who started it, whose fault it is. Tell them they have a choice about whether to resolve their disputes and enjoy their free time or carry on fighting, and that it is up to them to decide. They are likely to respond that they want to play but the other one wants to fight -- again, tell them they have a choice, and repeat as often as necessary.
Do not intervene no matter how much of a racket you hear in the background. Get yourself some earplugs. Let the chips fall where they may.