Well,
Having done both, I can tell you that this is a very tough argument. But I believe that they are both a very challenging and unique sport in their own right. Both cheerleading and ballroom dance have a set of rules and regulations, in both you are able to compete against other "teams." Both require countless hours of training and dedication.
For someone to say that one is more of a sport without every doing the other, it is natural for them to choose the one that they are doing, as they do not have the knowledge or experience to make an accurate judgment of the other.
I'm sure that most everyone who posts on this site would have no argument that ballroom dance is a focused sport. Challenging, physically demanding etc. etc. But for those who have never done cheerleading, I can tell you that between the stunts, flips, Jumps, HOURS upon HOURS spent to be sure every move you make is in synch with the rest of the team, even working out the sound of your voice to match your teammates pitch Yes, even hours spent on technique..It is also a VERY mentally and physically demanding sport.
My personal opinion is that this is a draw. One could argue either side endlessly because there is so much that goes into being a dancer or being a cheerleader. In my opinion, it is like arguing the sport merit of football vs. basketball. they are both sports right? And how could anyone possibly argue otherwise?
Tootles!
Chiq.