FFM is certainly more accepted in the scientific community, but is not without critics. 

It fails to predict peoples behavior in specific contexts (ie people change their behavior in each context and therefore their 'personality' is not fixed by determined by the context - ie the context is a more powerful influence, and so predictor, of behavior). 

If it cannot predict behavior then it's not a valid theory of behavior. Ie, it's quackery. So you win that point again. Lol.

"...it appears that the currently popular FFM should be replaced with an expanded and altogether more inclusive model of dynamic personality structure. "
Boyle, GJ. p21

https://www.researchgate.net/publication/27826750_Critique_of_the_five-factor_model_of_personality