If I were to use stats for something like this, I'd have the character's overall power level act as a pool of stat points to distribute among a small number of stats. 

- Stamina (acts as HP, and in a way a character's resilience in combat; high stamina is basically a defensive tank). 
- Strength (in a nutshell, physical attack power). 
- Speed (accounts for reaction time in combat, to achieve blocks and dodges). 
- Ki (goes into Ki-based attacks; your Kamehamehas and Galick Guns, and the ability to raise other stats). 

Maybe I got lost in the previously presented stat system, and mine is basically the same thing. The only hitch with any stat system is that it has to have a tangible function in practice. I wouldn't worry so much about people trying to raise their numbers up over each other because that can be moderated easily enough. An award system for participating in major combative events would suffice. Plus, then we could start applying transformations and fusions with some outlook on power. 

But then, I also kind of like Atomic's idea of using tiers. Tiers in tandem with cooperation from members, and, IMO, a willingness to accept some defeats to characters such as major villains in the first bouts when necessary, if we do drift in that direction.