Keep it simple and expect to answer the same questions over and over in the next few weeks. Kids take time to process things and will keep asking and will actually be comforted by the answers being consistent.
No matter what reason you give, the dogs are still gone and your little one will be upset so expect a tearful reaction. Don't keep offering more and more info in an attempt to stop the tears. Let your child be sad, tell them you're sad too, and give them lots of time to grieve and process what's happened. Answer the questions that get asked without overloading them with info.
You can tell him that there was an accident and the little dog was hurt very badly. His body wasn't strong enough after the accident and he died. Depending on your religious preferences, you can say he's now in doggie heaven or you can give him a simplified version of the "Rainbow Bridge" story, which is actually a kind of sweet story that kids tend to like.
I am very sorry for your loss and it's never easy to lose a furry member of the family. I do think it's okay for your child to see you being sad as it will help validate his feelings.
You can also have a little service - release a balloon up to heaven, draw a picture of the dog, plant a little tree, something that will help your child have some closure.
ETA - As far as the big dog being out of the house, I personally would tell my son that the big dog was part of the accident, he's very sad about what happened, and he's staying at the other house so that an accident like that doesn't happen again. Granted, that's just me - but I would not say the big dog killed the little dog as that's not a fact I'd want my kids obsessing over. I would expect my kids to insist the big dog come back so be prepared for that. If it came down to it, I'd say that this is the way it is for "grown up reasons". At that age, they don't necessarily need all the details.