I'd have to vote for with; if you shot at antimatter targets, the targets would likely self-destruct from contact with the air after launching (assuming an appropriately airless launching area, of course), removing the entire point of the sport. If, on the other hand, you used antimatter shot, you might get a cone of super-heated partially annihilated air between you and the target, making it look as if you destroyed it with a cone of laser beams emanating from the mouth of the gun. Sounds like pure awesome to me.
Wouldn't the shot and skeet have the same self-destructive problems? This seems better to do on the moon. Also, the low gravity would give you longer to fire.
Actually, I take that back too. You want to be doing this not only in a vacuum, but firing from REALLY FAR AWAY, because of the c^2 in E = mc^2 being big. So, maybe remote-controlled missiles of some sort.
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