I have the same rule as you, LR. I've always thought, if someone asks me to choose, then I choose the other person. Even if I would have preferred the first one, all things considered. Because I'll pick the one who isn't making me choose. I pick the one who isn't putting me in that situation, who will have me the way I am.
It seems only fair to me.
In your case, they've both asked you, it seems, so I'm not sure what you could do. Picking neither could be the more "fair" route, but then you have nobody left...
On the other hand I guess I wouldn't trust people very much if they were putting me in this situation to begin with. And rather than resent them forever, no matter which I chose, I might prefer to part ways completely.
I guess I'm not help at all. It sounds like a very hard situation.