It's been three years since I first answered. I made a good choice last time, at least when it comes to kettlebell exercises. I've become more fond of the barbell lately, and I think the barbell clean and jerk would win this time around.
But I think adding the clean is cheating. Like
@jef posted earlier on, it doesn't make sense to make it so that an exercise counts if one doesn't let go of the implement, because that would lead one to pick a circuit of an exercise... like the clean and the press or the clean and the jerk.
I think there is great value in the swing and the clean, no matter the tool, but I have to also confess that doing only either of those exercises would mean that I wouldn't train or exercise that much. I work better in slow gear.
These days I would pick the squat or the deadlift. Barbell would be the tool of choice, because of incremental loading, and, well, loading. I believe the deadlift would be the last man standing, and I would make it a bit harder; do it with a deficit, or with a wide grip, or both.
Snatch grip deficit deadlift it is.