once a dog has killed it becomes more difficult to stop this. still not impossible. i breed pit bulls for catching wild hogs and my dogs wont touch one of my birds.
first off you said they are high energy dogs, well, are you doing anything to help burn off some of this energy? walks, treadmills, anything?
next off are you the leader of the pack? more importantly does the yard belong to you or your dogs... in their mind, i mean.
what i would do is try only ONE dog at a time with this... short leash.
go for a walk, then take the dog in the vicinity of your birds allow it to look at them and get all antsy, then what ever noise u make to indicate no, do it loud and like its your world. what ever noise u make thats the universal noise wether no or i say "aop" followed by "you better get outta there. scold them tuff. make em lay down. and dont let them look at your birds now. get inbetween the birds and your dog with your body. basicly dont let them have what they want. dont let em get up till they are CALM. if you got to grab em by the back of their neck and force them to the ground do it. hold them till CALM. this excersise aint over till they show CALMNESS. claim your birds as your own property like a dominant dog would a ball. once they show calmness allow them to go from lay to sit. then remove them from being able to see birds. do other dog the same. you dont want to "overtrain" a dog. once or twice a day is good. if you over do it they will get stressed out and unlearn what you have worked hard to do.
over time allow the dog a longer and longer leash and allow them to roam futher from you. many people say dont hit your dog but i swat their snout and when i raise my hand my dogs bow dow. you dont always have a rolled up newspaper in hand. a switch works good to. once they good a good sting just the sound of a switch cutting air gets their attention. this may take days, weeks or months. depends on the dog and depends on you. dont be suggestive in tone with them, be stern.
all in all you must weigh whats good for you first and then the dogs. if you arent good at training dogs i recommend rehoming them. but i would bet dollars to pesos you can do it.
i train dogs so if what i wrote dont make cents or u need more help send me a message on here and i will get back at you. i dont have access to a computer all the time so it may take a few days er so.
edit: i just read what others said about keeping your dogs seperate, only do this when you are breaking them, if you seperate them all the time it will cause, in thier mind TWO packs which can bring on more problems, seperation anxiety, stress, etc. and once you are confident they are broken of chicken killing take both on a leash at same time outside. if they are not basic trained now is a good time to start(sit stay lay come all that