Chip and Dale could throw things at each other, but there was no point in doing so. The one losing a life wasn't the enemy, but the chipmunk being thrown. Unless I remember correctly, there was one instance in the second part where you had to throw the second chipmunk into a gap so that he could open a passage to throw a basketball.
Added 4 minutes later
And in Battle Toads, I didn't even know that I was already almost at the end, and, as I understand from the video, passing that level is much, much easier than passing the level with the boss at the very end of Battle Toads Double Dragon. In Battle Toads Double Dragon, it was really tough. I only managed to pass it on the last square with all my remaining strength!