I've been following this thread and I see everyone's point of view. But I think we need to make this question more specific. Are we talking about which surface is safer in regards to strictly falling from stunting or tumbling or are we talking about landing tumbling and the actual, overall performance? And are we talking about competitions, practice or games? It's kind of like comparing apples to oranges. Both are fruit, but they are very different.
Its obvious that if you're learning a tumbling skill than a crash mat or some sort of landing mat is the safest to learn it on when moving the skill to floor. But can you tumble on a crash mat like you can on a hard/spring floor? No, it's made to absorb almost ALL of the force you are putting into it. So would this be ideal for competition or even games? Most definitely not, you'd be hindered in every way possible.
So if the question is: What is the safest performance surface AT PRACTICE WHILE LEARNING A NEW SKILL, then its crash mat. If the question is What is the safest performance surface AT COMPETITION, then obviously a spring floor. But the very first question is too broad to be discussed properly. People are going all over the place here. Coaching has NOTHING to do with the performance floor and whether or not an athlete is going to get hurt when he or she hits it. A fall is a fall is a fall, no matter if you're a first time cheerleader or a member of the Olympic gymnastics team who decided to join F5. (New rumor? :P ) I also think we need to break it down into all star and high school/rec. For all stars, the question could still be "which is the safest....." but for high school, it might have to turn into "which is the most practical...." This is a very situational topic that wont have the same answer for every aspect of cheer. Just my opinion...