"The next time this round the target creature makes a melee attack, if that attack is not a Counterstrike, at the end of that attack action it may immediately make another quick action melee attack. This extra attack counts as part of the same attack action. Only one Battle Fury spell may be cast per round on the same creature."
That is the full text from Battle Fury. The part about being a part of the same attack action makes it exactly the same as double strike, triple strike, AND sweeping. It simply means that it can not benefit from things like melee +X a second time. It has nothing to do with targeting.
The part about being at the end of the attack action means that it occurs during Step 8: Attack Ends, and not during Step 5: Additional Strikes. This makes it even more similar to Sweeping than Doublestrike.
In the end though, the key thing to look for is the total lack of any targeting restriction in the text. If it doesn't restrict your target, then you can choose your target.