Perhaps start rewarding them for good behavior, and/or working out their differences themselves. I'm sure part of the problem, part of what makes you feel most drained, is that *you* have to be the judge; but if you can get them to handle squabbles themselves, they will feel more accomplished, as if they have more control over their lives (they are growing into men, after all, and need this affirmation), and as if they *can* do it.
I'd suggest having a family conference (or perhaps just your husband and the two boys would be better), and have your husband tell the boys that they're old enough to work out their own problems, and you shouldn't have to be the arbiter. Perhaps they need a few minutes in the meeting, or adjourn the meeting for a half-hour or until the next day, to give them time to come up with some solutions on how they can work on their problems, other than just fighting. They'll probably come up with some good solutions -- some might even surprise you with their ingenuity. But if they don't, or if their "solution" isn't workable (something like, "the offending brother has to stick his head in the toilet while the other brother gets to flush," or some similar immature solution), then you need to be prepared with some of your own. Chore charts, in which you divide tasks evenly between the brothers, have them switch off weeks, or whatever, will help with fighting over who has to feed the dogs, or take them out, or load the dishwasher, or clean the kitchen; and switching off even and odd days for when they get the preferred *whatever* [seat in the car or on the couch, or what program to watch when, or any other trivial matter]. Tell them that they can switch off preferences, if they both agree to it -- say it's the 15th of the month, so it's A's turn to pick what TV show to watch after school, but he traded with B, so that A got to ride in the "best" car seat on the way home from school, and let B pick the TV show.
You can use "the carrot and the stick" approach -- if they last a day or a week without you having to interfere (and without them bickering too much, or coming to blows, or whatever), then they get to stay up an extra half-hour or hour that night, or get to rent a movie that weekend or have a sleepover. But if they don't, then they'll lose half an hour of TV time, or can't stay up late on the weekends. Or something like that. Different kids have different "weak spots" -- your boys may be more affected by losing money if they argue than losing TV/computer/game time. Find out what motivates them (positively or negatively), and use it to your advantage. :-)
It will probably take some guidance from you, and it probably won't be an overnight success, but I think it will help. [I'm trying to do something similar with my boys, although they're younger so I'm still having to intervene more than I'd like. But I read about this approach several years ago from a seasoned mom, and I like it -- it has a worthy goal, and that's what I'm trying to reach.]